This is the basic and conceptual question from Chapter name- circles

Topic – Angle properties of circles

Chapter number- 15

In the given that ABC is an isosceles triangle in which AB = AC and circle passing through B and C intersects sides AB and AC at points D and E

We have to prove that DE || BC.

ICSE Avichal publication

Understanding ICSE Mathematics

Question 14

Solution:In the given figure,

∆ABC is an isosceles triangle in which AB = AC.

A circle passing through B and C intersects

sides AB and AC at D and E.

To prove: DE || BC

Construction : Join DE.

∵ AB = AC

∠B = ∠C (angles opposite to equal sides)

But BCED is a cyclic quadrilateral

Ext. ∠ADE = ∠C

= ∠B (∵ ∠C = ∠B)

But these are corresponding angles

DE || BC

Hence proved.