Question

In the given figure, AB and CD are two parallel chords of a circle. If BDE and ACE are straight lines, intersecting at E, prove that △ AEB is isosceles.

Answer 1

It is given that AB and CD are two parallel chords of a circle. If BDE and ACE are straight lines, intersecting at E

We know that in a cyclic quadrilateral exterior angle is equal to the interior opposite angle.

It can be written as

Exterior ∠EDC = ∠A

Exterior ∠DCE = ∠B

We know that AB || CD

So we get

∠EDC = ∠B and ∠DCE = ∠A

We get

∠A = ∠B

Therefore, it is proved that △ AEB is isosceles.