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In the figure, OP is equal to the diameter of the circle. Prove that ABP is an equilateral triangle. Asked by Topperlearning User | 27 Jul, 2017, 01:09: PM Expert Answer OP = 2r………given,OP= diameter of the circle OAP = 90o (Tangent is to the radius through the point of contact)

In right OAP

sin ( OPA) =   OPA = 30o

Similarly OPB = 30o  APB = 30o + 30o = 60o

Since PA = PB (Lengths of tangents from an external point are equal)  PAB = PBA

In APB, APB + PAB + PBA = 180o (angle sum property) 60o + 2 PAB = 180o  PAB = 60o  PBA = 60o

Since all angles are 60o, ABP is equilateral triangle.

Answered by | 27 Jul, 2017, 03:09: PM

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