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  1. Chapter 11 Class 10 Constructions
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Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60 . Concept Given angle between tangents is 60 i.e. QPR = 60 OQR = 2 60 = 120 So, we need to draw OQR = 120 Also, OQ QP & OR PR Thus, to make tangents, we draw perpendiculars from point Q and R Ex 11.2, 4 Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60 . The tangents can be constructed in the following manner: Draw a circle of radius 5 cm with centre O. We need make angle of 120 at center Draw diameter QOA Draw OAR = 60 Thus, QOR = 180 OAR = 180 60 = 120 Therefore, our two tangents will touch the circle at Q and R Now, we know that tangent is perpendicular to radius. Draw perpendicular from point Q and point R Let P be point where both perpendiculars intersect Thus, PQ and PR are the required tangents at angle of 60 Justification We need to prove PQ and PR are tangents and QPR = 60 Since PQ is perpendicular to OQ (radius) PQ must be a tangent Also, PR is a tangent Now, we need to prove QPR = 60 Since PQ OQ, OQP = 90 Also, PR OR, ORP = 90 and QOR = 120 Now, in quadrilateral OQPR QPR + PQO + PRO + QOR = 360 QPR + 90 + 90 + 120 = 360 QPR + 300 = 360 QPR = 360 300 QPR = 60 Thus, angle between tangents is 60 Now, in quadrilateral OQPR QPR + PQO + PRO + QOR = 360 QPR + 90 + 90 + 120 = 360 QPR + 300 = 360 QPR = 360 300 QPR = 60 Thus, angle between tangents is 60

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.