Mathematics
Prove that the tangents at the extremities of any chord make equal angles with the chord.
Circles
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Answer
Let AB be a chord of a circle with centre O, and AP, BP be the tangents at A and B respectively.
From figure,
PA = PB [∵ Tangents from an external point to a circle are equal]
In triangle PAB,
∠PAB = ∠PBA [Angles opposite to equal sides in a triangle are equal]
∴ ∠PAC = ∠PBC.
Hence, proved any chord make equal angles with the chord.
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