Mathematics
In the adjoining figure, △ABC is isosceles with AB = AC. Prove that the tangent at A to the circumcircle of △ABC is parallel to BC.
Circles
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Answer
In △ABC,
AB = AC (Given)
∴ ∠C = ∠B (∵ angles opposite to equal sides are equal.)
From figure,
∠TAC = ∠B (∵ angles in alternate segment are equal.)
But ∠B = ∠C
∴ ∠TAC = ∠C
But angles ∠TAC and ∠C are alternate angles. Since, they are equal
Hence, proved that AT || BC.
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