Question

In fig., two equal chords AB and CD intersect each other at E. Prove that arc DA = arc CB

Answer 1

Given :

Two equal chords AB and CD intersecting of point E. 

Let O be the centre.

To Prove :

arc DA = arc CB

⇒ ∠AOD = ∠COB

Construction : Through O join OA, OB, OC and OD

Proof : We know that corresponding arcs of equal chords are equal.

We know that same arcs subtends equal angles at center.

[∵ We know that same arcs subtends equal angles at centre.]