This is an important and exam oriented question from Chapter name- circles

Topic – Angle properties of circles

Chapter number- 15

It is given that ED and BC are two parallel chords of the circle and ABE, ACD are two st. lines.

We have to Prove that AED is an isosceles triangle.

ICSE Avichal publication

Understanding ICSE Mathematics

Question 13(a)

Solution:(a) Given: Chord BC || ED,

ABE and ACD are straight lines.

To Prove: ∆AED is an isosceles triangle.

Proof: BCDE is a cyclic quadrilateral.

Ext. ∠ABC = ∠D …(i)

But BC || ED (given)

Hence AED is isosceles triangle