In the given figure ∆ABC is an isosceles triangle in which AB = AC and a circle passing through B and C intersects AB and AC at D and E respectively. Prove that DE || BC.

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Solution

ABC is an isosceles triangle.
Here, AB = AC
∴ ∠ACB = ∠ABC ...(i)
So, exterior ∠ADE = ∠ACB
= ∠ABC [from(i)]
∴ ∠ADE = ∠ABC (Corresponding angles)
Hence, DE || BC

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