From an external point

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

P

, two tangents

PA

and

PB

are drawn to a circle with centre

O

. The chord

AB

is also drawn. (i) Prove that

\triangle OAP \cong \triangle OBP

and hence show that

OA = OB

. (ii) If

\angle APB = 60^\circ

, find the measure of

\angle AOB

. (iii) Is the quadrilateral

AOBP

cyclic? Give a reason for your answer.