Theorem 10.2: Equal tangents from external point (numerical type)

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Ex 10.2,3 Choose the correct option and give justification. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80 , then POA is equal to (A) 50 (B) 60 (C) 70 (D) 80 Given: PA and PB are tangents to circle & APB = 80 To find: POA Construction: Join OA,OB & OP Proof: Since PA is tangent, OA PA OAP = 90 In OAP & OBP OA = OB PA = PB OP = OP OAP OBP So, OPA = OPB So, OPA = / APB = 1/2 80 = 40 In OPA POA + OPA + OAP = 180 POA + 40 + 90 = 180 POA + 130 = 180 POA = 180 130 = 50 So, A is the correct answer

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.