ABC is an isoscles triangle in which AB=AC. A circle passing through B and C intersects the sides AB and AC at D and E respectively then show that DE is parallel to BC?

1 Answer
Jun 1, 2018

see explanation.

Explanation:

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Given AB=AC, => angleABC=angleACB
Let angleABC=x, => angleACB=x
As BCED is a cyclic quadrilateral, opposite angles add up to 180^@,
=> angleBDE=180-angleECB=180-x,
=> ADE=180-angleBDE=180-(180-x)=x
as angleADE=angleABC=x,
=> DE // BC