Question

Prove that the line joining the centre O of a circle to an exterior point P bisects the angle between the tangents drawn to the circle from the point P.

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Answer 1

Answer: Hence Proved

Step-by-step explanation:

By Tangent Theorem

A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

Tangent segment theorem

Tangent segments to a circle from a point outside the circle are concurrent.

ΔPAO ≡ ΔPBO     By property SSS

∠APO = ∠BPO

OP Bisects ∠APB

Hence It is proved