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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.

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, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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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