Question

From an external point, two tangents are drawn to a circle. Prove that the line joining the external point to the centre of the circle bisects the angle between the two tangents.

Answer 1

Draw a circle with centre O and take an external point P.

PA and PB are the tangents.

Join OP.

Now in ΔOAP and ΔOBP,

OA = OB   ...(Radius of circle)

OP = OP   ...(Common)

PA = PB   ...(Tangents are equal)

So, by S.S.S criteria,

ΔOAP ≅ ΔOBP

So, ∠APO = ∠BPO

Hence, OP bisects ∠APB.