prove that diameter is the longest chord in the circle

In an isosceles triangle ABC with AB = AC a circle passing through B and C intersect the sides AB and AC at D and E respectively.Prove that DE||BC.

 ulike model test paper 4 solutions

Prove that equal chords of a circle subtend equal angles at the centre.

prove that bisectors of angles formed by producing opposite sides of cyclic quadrilateral (provided they are not parallel) intersect each other at right angle.