Question

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?

Answer 1

see explanation.

Explanation:

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`