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Geometry(All Questions), SSC CGL 2020-21 Tier-1, , By Shubham Jain (RBE), Video-solution linkComplete playlist of SSC CGL 2020 Tier-1 Solutionhttps://youtube.com/playlist?list=PL5SDlP42gG0gVuqzSu33ufwAu2CRNQUcN, Telegram Channel link for All chapters pdfs- https://t.me/RBE_S, Q.1 In ΔABC, ∠A = 90°, AD⊥BC at D. If AB = 12 cm and AC = 16 cm, then what is the length (in cm) of BD?, (a) 8.4, (b) 7.8, (c) 7.2, (d) 6.4, Q.2 In triangle ABC, D is a point on BC such that BD : DC = 3 : 4. E is a point on AD such that AE : ED = 2 : 3., Find the ratio 𝑎𝑟𝑒𝑎 (𝛥𝐸𝐶𝐷): 𝑎𝑟𝑒𝑎 (𝛥𝐴𝐸𝐵)., [a] 9 : 8, (b) 1 : 2, (c) 2 : 1, (d) 8 : 9, Q.3 The angles of a triangle are in AP (arithmetic progression). If the measure of the smallest angle is 50°, less than that of the largest angle, then find the largest angle (in degrees)., [a] 80, (b) 85, (c) 90, (d) 75, Q.4 ΔABC∼ ΔPQR. The areas of ΔABC and ΔPQR are 64 cm² and 81 cm², respectively and AD and PT are the, medians of ΔABC and ΔPQR, respectively. If PT = 10.8 cm, then AD = ?, (a) 8.4 cm, (b) 9 cm, (c) 9.6 cm, (d) 12 cm, Q.5 A chord 21 cm long is drawn in a circle of diameter 25 cm. The perpendicular distance of the chord, from the centre is:, (a) √41, (b) √23, (c) √56, (d) √46, 𝑎𝑟(𝛥𝐴𝐵𝐶), 144, Q.6 Let ΔABC～ΔPQR and, =, . If AB = 12 cm, BC = 7 cm and AC = 9 cm, then PR (in cm) is equal, 𝑎𝑟(𝛥𝑃𝑄𝑅), , 49, , to:, (a) 12, (b) 49/12, (c) 108/7, (d) 21/4, Q.7 In a triangle ABC, a point D lies on AB and points E and F lie on BC such that DF is parallel to AC and DE, is parallel to AF. If BE = 4 cm, EF = 6 cm, then find the length (in cm) of BC., (a) 25, (b) 30, (c) 15, (d) 20, Q.8In a triangle ABC, point D lies on AB, and points E and F lie on BC such that DF is parallel to AC and DE is, parallel to AF. If BE = 4 cm, CF = 3 cm, then find the length (in cm) of EF ?, (a) 3, (b) 1.5, (c) 5, (d) 2, Q.9 From an external point A, two tangents AB and AC have been drawn to a circle touching the circle at B, and C respectively. P and Q are points on AB and AC respectively such that PQ touches the circle at R. If AB, = 11 cm, AP = 7 cm and AQ = 9 cm, then find the length of PQ (in cm)., (a) 8, (b) 7, (c) 5, (d) 6, Q.10 In a circle with center O, AB is a diameter and CD is a chord such that ∠ABC = 34° amd CD = BD. What, is the measure of ∠DBC?, (a) 30°, (b) 24°, (c) 32°, (d) 28°, Q.11 In a trapezium PQRS, PQ is parallel to RS and diagonals PR and QS interesect at O. If PQ = 4 cm, SR =, 10 cm, then what is the area(ΔPOQ) : area(ΔSOR)?, (a) 4 : 25, (b) 2 : 3, (c) 4 : 9, (d) 2 : 5, Q.12 In a circle with center O and radius 5 cm, AB and CD are two parallel chords of lengths 6 cm and x cm,, respectively and the chords are on the opposite side of the centre O. The distance between the chords is 7, cm. What is the value of x?, (a) 12, (b) 8, (c) 10, (d) 9

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Q.13 In a circle with centre O, AB and CD are two parallel chords on the same side of the diameter. If AB =, 12 cm, CD = 18 cm and distance between the chords AB and CD is 3 cm, then find the radius of the circle (in, cm)., (a) 15, (b) 12, (c) 3√13, (d) 9, Q.14 In a circle with centre O, AB and CD are parallel chords on the opposite sides of a diameter. If AB = 12, cm, CD = 18 cm and the distance between the chords AB and CD is 15 cm, then find the radius of the circle, (in cm)., [a] 3√13, (b) 9, (c) 9√13, (d) 12, Q.15 The side of equilateral 𝛥ABC is 3√7 cm. P is a point on the side BC such that BP : PC = 1:2. The length, (in cm) of AP is:, [a] 6√3, (b) 7√3, (c) 6, (d) 7, Q.16 ΔABC is an equilateral triangle. D is a point on the side BC such that BD : BC = 1 : 3. If, AD = 5√7 cm, then the side of the triangle is:, (a) 18 cm, (b) 12 cm, (c) 20 cm, (d) 15 cm, 1, [Q].17 Δ ABC is an equilateral triangle with side 18 cm. D is a point on BC such that BD = BC. Then length (, 3, in cm) of AD is:, [a] 6√3, (b) 6√7, (c) 7√6, (d) 8√3, Q.18 In ΔABC, DE∥AB, where D and E are the points on sides AC and BC, respectively. If AD = x-3, AC = 2x,, BE = x-2 and BC = 2x+3, then what is the value of x?, (a) 12, (b) 10, (c) 8, (d) 9, Q.19 In ΔABC, D is the midpoint of side AC and E is a point on side AB such that EC bisects BD at F. If AE =, 30 cm, Then the length of EB is:, (a) 10, (b) 20, (c) 15, (d) 18, Q.20 Sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E and sides AD and BC are, produced to meet at F. If ∠ADC = 78° and ∠BEC = 52°, then the measure of ∠AFB is:, (a) 26°, (b) 32°, (c) 30°, (d) 28°, Q.21 If one of the angles of a triangle is 74°, then the angle between the bisectors of the other two interior, angles is:, (a) 127°, (b) 16°, (c) 53°, (d) 106°, Q.22 Angle between the internal bisectors of two angles ∠B and ∠C of a ΔABC is 132°, then the value of ∠A, is:, (a) 84°, (b) 62°, (c) 48°, (d) 72, Q.23 ABCD is a cyclic quadrilateral. AB and DC meet at F, when produced. AD and BC meet at E, when, produced. If ∠BAD = 68° and ∠AEB = 27°, then what is the measure of ∠BFC?, (a) 27°, (b) 22°, (c) 15°, (d) 17°, Q.24 ΔABC is inscribed in a circle with center O, such that ∠ACB = 115°, O is joined to A. What is the, measure of ∠OAB?, (a) 30°, (b) 20°, (c) 25°, (d) 35, Q.25 AB is the diameter of a circle. C and D are points on the opposite sides of the diameter AB, such that, ∠ACD = 25°. E is a point on the minor arc BD. Find the measure of ∠BED, (a) 115°, (b) 105°, (c) 130°, (d) 125°, Q.26 A chord AB of circle C1 of radius 17 cm touches circle C2 which is concentric to C1. The radius of C2 is, 8 cm. What is the length (in cm) of AB?, (a) 30, (b) 25, (c) 20, (d) 24, [Q].27 In ΔABC, ∠A = 50°. If the bisectors of the angle B and angle C, meet at a point O, then ∠BOC is equal, to:, [a] 130°, (b) 65°, (c)50°, (d) 115°, [Q].28 In triangle ABC, AD is the bisector of ∠A. If AB = 5cm, AC = 7.5cm and BC = 10cm, then what is the, distance of D from the midpoint of BC (in cm)?, [a] 2, (b)1.5, (c) 2.2, (d) 1, [Q].29 Vertices A, B , C and D of a quadrilateral ABCD lie on a circle. ∠A is three times ∠C and ∠D is two, times ∠B. What is the difference between the measures of ∠D and ∠C?

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[a] 55°, (b) 65°, (c)75°, (d) 45°, [Q].30 A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC, CD and DA at P, Q , R and S,, respectively. If AS = 6cm, BC = 12 cm, and CR = 5 cm, then the length of AB (in cm) is:, [a] 13, (b)11, (c) 15, (d) 12, [Q].31 Triangles ABC and DBC are right angled triangles with common hypotenuse BC. BD and AC intersect, at P when produced. If PA = 8 cm, PC = 4cm and PD = 3.2 cm, then the length of BD, in cm is:, [a] 5.6, (b) 7.2, (c)6.4, (d) 6.8, Q.32 The bisector of ∠A in ΔABC meets side BC at D. If AB = 12cm, AC = 15 cm and BC = 18cm, then the, length of DC is:, [a] 9 cm, (b) 6 cm, (c)10 cm, (d) 8 cm, Q.33 ABCD is a cyclic quadrilateral in which ∠A = x°, ∠B = 5y°, ∠C = 2x° and ∠D = y°. What is the value of (3x, - y)?, [a] 120, (b) 60, (c)90, (d) 150, 1, Q.34 In ΔABC , D is a point on BC such that ∠BAD = ∠ADC and ∠BAC = 77° and ∠C = 45°. What is the, 2, measure of ∠ADB ?, [a] 64°, (b) 77°, (c) 45°, (d) 58°, Q.35 A tangent is drawn from a point P to a circle, which meets the circle at T such that PT = 8cm. A secant, PAB intersects the circle in points A and B. If PA = 5cm, what is the length (in cm ) of the chord AB?, [a] 6.4, (b) 8.4, (c) 7.8, (d)8.0, Q.36 In the triangle ABC, D and E are the mid points of AB and BC respectively. If area(ΔCED) = 8 cm² then, what is the area (ADEC) in cm²?, [a] 21, (b) 32, (c)24, (d) 16, Q.37 The area of a table top in the shape of an equilateral triangle is 9√3 cm². What is the length ( in cm) of, each side of the table?, [a] 6, (b) 2, (c)4, (d) 3, Q.38 Let ΔABC 〜 ΔRPQ and, , 𝑎𝑟(△ 𝐴𝐵𝐶), 𝑎𝑟(△ 𝑃𝑄𝑅), , =, , 16, 25, , . If PQ = 4 cm, QR = 6cm and PR = 7cm, then AC (in cm) is equal, , to:, [a] 7.2, (b) 6, (c)4.8, (d) 5.6, Q.39 In a triangle ABC, length of the side AC is 4 cm more than 2 times the length of the side AB. Length of, the side BC is 4 cm less than the three times the length of the side AB. If the perimeter of ΔABC is 60 cm,, then its area (in cm²) is:, [a] 120, (b) 150, (c)144, (d) 100, Q.40 ABCD is a cyclic quadrilateral such that when sides AB and DC are produced, they meet at E, and, sides AD and BC meet at F, when produced. If ∠ADE = 80° and ∠AED = 50°, then what is the measure of, ∠AFB?, [a] 30°, (b) 40°, (c)20°, (d) 50°, Q.41 The vertices of a ΔABC lie on a circle with centre O. AO is produced to meet the circle at the point P. D, is a point on BC such that AD ⏊ BC. If ∠B = 68° and ∠C = 52°, then the measure of ∠DAP is:, [a] 28°, (b) 16°, (c)12°, (d) 18°, Q.42 In a triangle ABC, AB : AC = 5:2. BC = 9 cm. BA is produced to D, and the bisector of the Angle CAD, meets BC produced at E. What is the length (in cm) of CE?, (a) 9, (b) 10, (c) 6, (d) 3, Q.43 In ΔABC, D and E are the points on sides AB and AC, respectively such that ∠ADE = ∠B. If AD = 7 cm,, BD = 5 cm and BC = 9cm, then find DE (in cm)., (a) 6.75, (b) 10, (c) 5.25, (d) 7, Q.44 In a circle with centre O, AD is diameter and AC is chord. Point B is on Ac such that OB = 7cm and, ∠OBA = 60°. If ∠DOC = 60°, then what is the length of BC (in cm)?, (a) 7, (b) 9, (c) 5, (d) 3.5, Q.45 ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 138° and ∠ECD, = 35°, then what is the measure of ∠BAC?, (a) 133°, (b) 103°, (c) 113°, (d) 123°

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Q 46 A circle touches all the four sides of quadrilateral ABCD whose sides are AB = 8.4 cm, BC = 9.8 cm, and, CD = 5.6 cm. The length of side AD, in cm, is:, (a) 4.9, (b) 4.2, (c) 3.8, (d) 2.8, Q47 In ΔABC, ∠C = 90° and Q is the midpoint of BC. If AB = 10 cm and AC = 2√10 cm, then the length of AQ, is:, (a) √55 cm, (b) 5√3 cm, (c) 5√2 cm, (d) 3√5 cm, Q.48 ΔABC ~ ΔDEF and the area of ΔABC is 13.5 cm² and the area of ΔDEF is 24 cm². If BC = 3.15 cm, then, the length (in cm) of EF is:, (a) 4.8, (b) 3.9, (c) 5.1, (d) 4.2, Q.49 The radii of two concentric circles are 12 cm and 13 cm. AB is a diameter of the bigger circle. BD is a, tangent to a smaller circle touching it at D. Find the length (in cm) of AD. (Correct to one decimal place), (a) 24.5, (b) 23.5, (c) 25.5, (d) 17.6, Q.50 ABCD is a cyclic quadrilateral such that AB is the diameter of the circle and ∠ADC = 145°, then what is, the measure of ∠BAC ?, [a] 35°, (b) 45°, (c) 65°, (d) 55°, Q. 51 Points P, Q, R, S and T lie in this order on a circle with centre O. If chord TS is parallel to diameter PR, and ∠RQT = 58°, then find the measure of ∠RTS., [a] 58°, (b) 29°, (c) 45°, (d) 32°, Q.52 In ΔABC, AD is the bisector of ∠A meeting BC at D. If AC = 21 cm, BC = 11 cm and the length of BD is 3, cm less than DC, then the length (in cm) of side AB is:, (a) 10, (b) 12, (c) 15, (d) 18, Q.53 In ΔABC, AD⊥BC at D and AE is the bisector of ∠A. If ∠B = 62° and ∠C = 36°, then what is the measure, of ∠DAE?, (a) 13°, (b) 54°, (c) 23°, (d) 27°, Q.54 AB is a chord of a circle in minor segment with center O, C is a point on the minor arc of the circle, between the points A and B. The tangents to the circle at A and B meet at the point P. If ∠ACB = 102°, then, what is the measure of ∠APB?, [a] 27°, (b) 29°, (c) 24°, (d) 23°, Q.55 Point P lies outside a circle with centre O. Tangents PA and PB are drawn to meet the circle at A and, B respectively. If ∠APB = 80°, then ∠OAB is equal to:, [a] 140°, (b) 40°, (c) 70°, (d) 35°, Q.56 Points A and B are on a circle with centre O. Point C is one the major arc AB. If ∠OAC = 35° and ∠OBC, = 45°, then what is the measure (in degrees) of the angle subtended by the minor arc AB at the centre?, [a] 80, (b) 70, (c) 100, (d) 160, Q.57 Points A and B are on a circle with center O. PAM and PBN are tangents to the circle at A and B, respectively from a point P outside the circle. Point Q is on the major arc AB such that ∠QAM = 58° and, ∠QBN = 50°, then find the measure of ∠APB., [a] 30°, (b) 32°, (c) 36°, (d) 40°, Q.58 In a circle with centre O, PAX and PBY are the tangents to the circle at points A and B, from an, external point P. Q is any point on the circle such that ∠QAX = 59° and ∠QBY = 72°. What is the measure of, ∠AQB?, (a) 31°, (b) 72°, (c) 59°, (d) 49°, Q.59 In a circle, a 10 cm long chord is at a distance of 12 cm from the centre of the circle. Length of the, diameter of the circle (in cm) is:, [a] 20, (b) 26, (c) 13, (d) 22, Q.60 In triangle ABC, P and Q are the midpoints of AB and AC. respectively. R is a point on PQ such that PR, : RQ = 3 : 5 and QR = 20 cm, then what is the length (in cm) of BC?, [a] 24, (b) 40, (c) 64, (d) 66.66, Q.61 In triangle ABC, D and E are the points on sides AB and AC, respectively and DE॥BC. BC = 8 cm and DE, = 5 cm. If the area of triangle ADE = 45 cm², then what is the area of triangle ABC?, (a) 105.2, (b) 115.2, (c) 64, (d) 125

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Q.62 In a right angled triangle ABC, the lengths of the sides containing the right angle are 5 cm and 12 cm, respectively. A circle is inscribed in the triangle ABC. What is the radius of the circle (in cm)?, [a] 2.8, (b) 3, (c) 2, (d) 2.5, Q.63 In ΔABC, AB and AC are produced to points D and E respectively. If the bisectors of angle CBD and, angle BCE meet at point O, such that ∠BOC = 63°, then ∠A = ?, [a] 54°, (b) 27°, (c) 63°, (d) 36°, Q.64 What is the length (in cm) of the smallest altitude of the triangle whose sides are 5 cm, 12 cm and 13, cm? (correct to one decimal place)?, [a] 5.1, (b) 12.0, (c) 4.6, (d) 2.6, Q.65 Chord AB of a circle of radius 10 cm is at a distance of 8 cm from the center O. If tangents drawn at A, and B interact at P, then the length of the tangent AP (in cm) is:, [a] 4, (b) 15, (c) 3.7565., (d) 7.5, Q. 66 𝛥𝐴𝐵𝐶 ∼ 𝛥𝐷𝐸𝐹. If the areas of 𝛥𝐴𝐵𝐶and 𝛥𝐷𝐸𝐹are 100 cm² and 81 cm², respectively and the, altitude of 𝛥𝐷𝐸𝐹is 6.3 cm, then the corresponding altitude of 𝛥𝐴𝐵𝐶is:, [a] 5.6 cm, (b) 9 cm, (c) 7 cm, (d) 8.4 cm, Q.67 AB is a chord of a circle with centre O and P is any point on the circle. If ∠APB = 122°, then what is, the measure of ∠OAB?, [a] 15°, (b) 28°, (c) 32°, (d) 22°, Q.68 Two circles of radius 15 cm and 37 cm intersect each other at the points A and B. If the length of a, common chord is 24 cm, what is the distance (in cm) between the centres of the circles?, [a] 45, (b) 42, (c) 44, (d) 40, Q.69 In a circle with centre O and radius 13 cm, a chord AB is drawn. Tangents at A and B intersect at P, such that ∠APB = 60°. If distance of AB from the centre O is 5 cm, then what is the length of AP?, [a] 22, (b) 24, (c) 11, (d) 12, Q. 70 Triangle ABC is an equilateral triangle. D and E are points on AB and AC respectively such that DE is, parallel to BC and is equal to half the length of BC. If AD + CE + BC = 30 cm, then find the perimeter (in cm), of the quadrilateral BCED., [a] 4, (b) 25, (c) 37.5, (d) 35, Q.71 In a circle, chords AB and CD intersect internally, at E. If CD = 16 cm, DE = 6 cm, AE = 12 cm and BE = x, cm then the value of x is:, [a] 17, (b) 5, (c) 9, (d) 6, Q.72 Points A, D, C, B and E are concyclic. If ∠AEC = 50°, and ∠ABD = 30°, then what is the measure (in, degrees) of ∠CBD?, [a] 15, (b) 30, (c) 20, (d) 10, Q.73 Two circles of radii 18 cm and 16 cm intersect each other and the length of their common chord is 20, cm. What is the distance (in cm) between their centres?, [a] 4√14 + 2√39, (b) 4√10 + 2√39, (c) 4√14 - 2√39, (d) 4√10 - 2√39, Q.74 Points P and Q are on the sides AB and BC respectively of a triangle ABC, right angled at B. If AQ = 11, cm, PC = 8 cm and AC = 13 cm, then find the length (in cm) of PQ:, [a] 4√7, (b) √15, (c) 4.5, (d) 4, Q.75 Points M and N are on the sides PQ and QR respectively of a triangle PQR, right angled at Q. If PN =, 9cm, MR = 7cm, and MN = 3 cm, then find the length of PR(in cm)., [a] 13, (b) 11, (c)12, (d) √41, Q.76 In a circle with centre O, a diameter AB is produced to a point P lying outside the circle and PT is a, tangent to the circle at a point C on it. If ∠BPT = 28°, then what is the measure of ∠BCP?, [a] 28°, (b) 31°, (c) 62°, (d) 45°, Q.77 Triangle ABC is right angled at B and D is a point of BC such that BD = 5 cm, AD = 13 cm and AC = 37, cm, then find the length of DC in cm., [a] 25, (b) 35, (c)5, (d) 30, Q.78 In a circle with centre O, points A, B, C and D in this order are concyclic such that BD is a diameter of, the circle. If ∠BAC = 22°, then find the measure (in degrees) of ∠COD., [a] 158, (b) 68, (c)79, (d) 136

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Q.79 Triangle ABC is right angled at B. BD is an altitude intersecting AC at D. If AC = 9cm and CD = 3cm,, then find the measure of AB (in cm)., [a] 3, (b) 6√3, (c) 6, (d) 3√6, Q. 80 Points A, B and C are on a circle with centre O such that ∠BOC = 84°. If AC is produced to a point D, such that ∠BDC = 40° , then find the measure of ∠ABD (in degree)., [a] 92, (b) 102, (c)56, (d) 98, Q. 81 In a circle with centre O, AB is a chord of length 10 cm. Tangents at points A and B intersect outside, the circle at P. If OP = 2 OA, then find the length (in cm) of AP., [a] 10, (b) 12, (c)12.5, (d)15, 𝐴𝐵 𝐵𝐶 𝐴𝐶, Q.82 In ΔABC and ΔDEF, we have = = , then which of the following is true?, [a] ΔDEF 〜 ΔABC, , 𝐷𝐹, , 𝐷𝐸, , 𝐸𝐹, , (b) ΔBCA 〜 ΔDEF, , 1. (c) 7.2, , 2. (c) 2 : 1, , 3. (b) 85, , 10. (d) 28°, , 12. (b) 8, , 19. (c) 15, , 11. (a) 4 :, 25, 20. (d) 28, , 28. (d) 1, , 29. (c)75°, , 30. [a] 13, , 37. [a] 6, , 38. (d) 5.6, , 39. [a] 120, , 46. (b) 4.2, , 48. (d) 4.2, , 55. (b) 40°, , 47. (a) √55, cm, 56. (d) 160, , 64. (c) 4.6, , 65. (d) 7.5, , 73. [a] 4√14 +, 2√39, , 74. (d) 4, , 82.(b) ΔBCA 〜, ΔDEF, , (c)ΔCAB 〜 ΔDEF, , (d) ΔDEF 〜 ΔBAC, , 4. (c) 9.6, cm, 13. (c), 3√13, 22. (a), 84°, 31. (d), 6.8, 40. [a], 30°, 49. (a), 24.5, 58. (d), 49°, , 5. (d) √46 6. (d), 21/4, 14. [a], 15. (d) 7, 3√13, 23. (d), 24. (c), 17°, 25°, 32. (c)10 33. (d), cm, 150, 41. (b), 42. (c) 6, 16°, 50. [a], 51. (d), 35°, 32°, 59. (b), 60. (c), 26, 64, , 7. (a) 25, , 8. (d) 2, , 9. (d) 6, , 16. (d) 15, cm, 25. (a), 115°, 34. [a] 64°, , 17. (b), 6√7, 26. (a), 30, 35. (c), 7.8, 44. (a) 7, , 18. (d) 9, , 61. (b), 115.2, , 45. (b), 103°, 53. (a), 54. (c), 13°, 24°, 62. (c) 2 63. [a], 54°, , 66. (c) 7, cm, , 67. (c), 32°, , 68. (c), 44, , 69. (b), 24, , 70. (c), 37.5, , 71. (b), 5, , 72. (c), 20, , 75. (b) 11, , 76. (b), 31°, , 77. (d), 30, , 78. (d), 136, , 79. (d), 3√6, , 80. (d), 98, , 81. [a], 10, , 21.(a)127°, , 57. (c) 36°, , 43. (c), 5.25, 52. (b) 12, , 27. (d), 115°, 36. (c)24