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he given circe F, with centre, 3 cm, -4 cm, ngents to the gie, Draw a pair of tangents to a circle of radius, 5 cm inclined to each other at an angle of 60°., Justification, Join AM and AP., [CBSE 2014], Similar question asked, il with radius = 4 cm, ii] with radius, iii with radius = 3 cm, Angle in a semicircle with, centre at O, |AMB = 90°, [SSLC April 2019|, [SSLC June 2019], [SSLC June 2020], %3D, 3.5 cm, %3D, AML BM, %3D, Steps of construction, AM radius of circle with centre A, Sol:, 11 With O as centre draw a circle of radius 5 cm., 21 Draw radii OP and OR such that |POR = 120°, 3] Draw RE OR., 41 Draw PD OP., 51 PD and RE meet at point N; RNP = 60°., So, BM = tangent from an external point B., Similarly BP is the tangent to the circle with, centre A., Join BN and BQ., |ANB = 90°, Angle in a semicircle with O as, the centre, Justification, By construction ORN =90°, and OR is the radius, and, RN is the tangent, AN I BN, BN = radius of the circle with centre B, Similarly OPN = 90° , OP is the radius and PN is the, tangent., So, AN = tangent from an external point A., ROP 120°, Construction, Similarly AQ is the tangent to the circle with centre B., ORN 1OPN= 90°, [9, Let ABC be a right-triangle in which AB 6 cm,, BC = 8 cm, and B = 90°. BD is the perpendicular, from B on AC. A circle through B, C, D is drawn., Construct the tangent from A to this circle., In quadrilateral ORNP, ROP+OPN+ORN+RNP = 360°, 120°+90°+90°+RNP = 360° → |RNP= 60°., [CBSE 2015, 2014], %3D, %3D, surement at, A., 6 cm, each at a dist, o09, Tangent, 8 cm, B., Draw a line segment AB of length 8 cm. Taking A as, centre, draw a circle of radius 4 cm and taking B as, centre, draw another circle of radius 3 cm. Construct, tangents to each circle from the centre of the other, circle., both sides, such that OF, [CBSE 2014], and 00 which, Sol, Sol:, Steps of construction, 1] Draw a line segment AB of length 8 cm., 2] Draw a circle with centre A and radius 4 cm, Steps of construction, 1] Draw the line segment AB = 6 cm and BC = 8 cm, perpendicular to each other. Join AC. ABC is the, constructed triangle., 2] Draw the perpendicular bisector of BC which, Sper se, %3D, %3D, and another circle with centre B and radius, 3 cm., gIven cirdeat, 3] Draw the perpendicular bisector of AB. Mark its, midpoint at O., 4] Take O as centre and AO as radius draw the, dotted circle and this intersects the two circles at, N, Q M, and P., J Join AN, AQ BM, and BP. These are the required, tangents to each circle from the centre of the other, circle,, meets BC at O., 3] With O as centre and OB as radius draw a circle, which intersects AC at D, Then, BDC = 90°. Thus, BD I AC with [BDC being the angle in the, FO Nd Wd, Sects the giver, given, semicircle,, 41 With A as centre and AB as radius draw an arc, cutting the circle at M., 51 Join AM; thus AB and the AM are required, MP is the a, tangents., M., Justification, Since AABC is right-angled:, BOL AB, BO radius of the circle, B., 4., AB tangent from external point A, w, CHAPTER 6, ZEN, Nov 23, 2021, 15:34