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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.
Solution
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.
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