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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.

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

Answers (1)


Given ABC is an isosceles triangle and AB = AC.

To Prove : XY\parallel BC
Proof: AB = AC     (Given)
\angle ABC= \angle ACB
[  The angle between the chord of a circle and tangent is equal to the angle made by the chord in an 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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