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FIRST PRELIMINARY EXAM, 2021-2022, GEOMETRY, Marks : 40, STD. :X, DATE : 20-12-2021, Time : 2 hrs., (04), Q1 A) Choose the correct alternative., 1.), In a right-angled triangle, if sum of the squares of the sides making right angle is, 169 then the length of the hypotenuse is, (C)5, (A) 15, (B)13, (D) 12, 2.), In A ABC, B-D-C and BD=7, BC=20 then, A(AABD), A(AADC), (A) 20, (B), (C), (D)0, A circle touches all sides of a parallelogram. So, the parallelogram must be a ., (A) rectangle (B) rhombus, 3), (C) square, (D) trapezium, Out of the following, point., (B) (0,2), 4), lies to the right of the origin on X- axis., (A)(-2,0), (C) (2,3), (D) (2,0), (04), B) Solve the following, 1.) If Sin 8=7/25, find the value of Cos e, 2) Construct a tangent to a circle with center P and radius 3.2cm at any point M on, it without using the center., 3.) The ratio of corresponding sides of similar triangles is 3:5; then find the ratio of, their areas., 4.) Find the length a diagonal of a rectangle having sides 11 cm and 60cm., Q.2 A) Complete the following activity. (Any two), (04), 1.) For finding AB and BC with the help of information given in the figure, complete, following activity., A, %23, AB BC, Given, . ZBAC, : AB = BC =, x AC, x 2/2, %3D, 1
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STD. : X, GEOMETRY, PAGE NO. 2, 2) In figure, chord EF|| chord GH. Prove that, chord EG chord FH., Fill in the blanks and write the proof., Proof: Draw seg GF., E, ZEFG = ZFGH, alternate angles (1), ZEFG =, . . Inscribed angle theorem (II), H,, ZFGH =, Inscribed angle theorem (III), .m (arc EG) =, from (1),(II), (III), . chord EG e chord FH, 20, If Cos 0=, 29, 3), Find the value of Sin 0., Using trigonometric identity., Solution:, Cos? 0 +, = 1, .: Sin? e = 1- Cos? 0, 400, .: Sin? 0 = 1-, 841-400, .. Sin? 0 =, .: Sin 0 =, (08), B) Solve the following: (any four), 1.), In figure, BC is perpendicular to AB, AD is perpendicular to AB,, BC = 4, AD = 8, then find, A(A ABC) / A(A ADB)., B, 2), Draw a circle of radius 2.7 cm. Draw a tangent to the circle at any point on it., 3.) Find the coordinates of midpoint of the segment joining the points P(0,6) and, Q(12,20)., SX, 2
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STD.: X, GEOMETRY, PAGE NO. 3, E, 4) In the fig, chords AC and DE intersect at B., If LABE = 108 m (arc AE) = 95°,, Find the m (arc DC)., D', 5) Find RP and PS, using the information given, in A PSR, P, 30, 6., Q.3 A) Complete the following activity (Any 1), 1) In the fig, seg AB is a diameter of a circle with, center O. The bisector of ZACB intersects the circle at point, D. Prove that seg AD = seg BD. Complete the following, proof by filling in the blanks., (03), A, B, Proof., ZACB = |BIC, Angle inscribed in semicircle., ZDCB =, CD is bisector of ZC., D, m (arc DB) =, Inscribed angle theorem., %3D, ZDOB = |2r, Definition of measure of an arc. (i), Seg OA = seg OB, :: Líne OD is, (ii), From (i) & (ii), of seg AB, .. Seg AD = seg BD, 2) In Trapezium ABCD side AB || side DC, diagonals, AC and BD intersect in point 0. If AB = 20, DC = 6, OB, = 15. Then complete the following activity to find OD., Sol:, In A COD and A AOB,, B, A, ZCDO LABO, ZCOD = LAOB, .A COD -AAOB, : OD = DC, C.S.s.t, :. OD = 6, : OD =, SX, 3
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GEOMETRY, STD. : X, PAGE NO. 4, B.) Solve the following (Any two), (06), Find the coordinates of point P if P divides the line segment joining the points, A (-1,7) and B (4, -3) in the ratio 2: 3., 1.), 2.) In the figure, M is the midpoint of QR. ZPRQ = 90°. Prove that, PQ2= 4PM2- 3PR?, R, Q, Prove that when two triangles are similar, the ratio of areas of those triangles, is equal to the ratio of the squares of their corresponding sides., 3.), 4.), Prove that :, Sec A (1 - Sin A) (Sec A + Tan A) = 1, %3D, (08), Q.4) Solve any two of the following, 1.) AAMT -A AHE. In A AMT, AM = 6.3 cm, ZTAM= 50°,, AM, AT = 5.6 cm,, АН, 7, Construct AAHE., 5, %3D, 2.) Find x if distance between points L (x, 7) and M (1, 15) is 10., 3.) In the adjoining figure the radius of a circle with center C is 6 cm, line AB is a, tangent at A. Answer the following questions., (1), What is the measure of ZCAB? Why?, (2), What is the distance of point C from line AB? Why?, (3), d (A, B) = 6 cm, find d (B, C)., (4), What is the measure of ZABC? Why?, • C, A, Q.5) Solve any one of the following., (03), 1) Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a, distance 7.3 cm from the center., 2) Prove that: If 5SecA - 12CosecA = 0, find the values of Sec A, Cos A and Sin A., * ****, 4
