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Write ‘True’ or ‘False’ and justify your answer in each of the following :The tangent to the circumcircle of an isosceles triangle ABC at A, in which AB = AC, is parallel to BC.

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Answer: true

Given ABC is a isosceles triangle and AB = AC.

To Prove : XY\parallel BC
  Proof : AB = AC     (Given)
\angle ABC= \angle ACB
[  angle between chord of a circle and tangent is equal to angle made by chord in alternate segment]
Also \angle XAB= \angle ABC
\Rightarrow \angle XAB= \angle BCA
\Rightarrow XAY\parallel BC
i.e , \Rightarrow XY\parallel BC
Hence true


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