CBSE Class 10 Answered

Say,Radius (OA) = r

OP = 2r………given,OP= diameter of the circle

OAP = 90^o (Tangent is to the radius through the point of contact)

In right OAP

sin (OPA) =

OPA = 30^o

Similarly OPB = 30^o

APB = 30^o + 30^o = 60^o

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

PAB = PBA

In APB,

APB + PAB + PBA = 180^o (angle sum property)

60^o + 2PAB = 180^o

PAB = 60^o

PBA = 60^o

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