Question

In fig., AB and CD are equal chords of a circle, with center O OM ⊥ AB and ON ⊥ CD then Prove that ∠OMN = ∠ONM

Answer 1

Given :

In circle C (O, r) chord AB = chord CD

and OM ⊥ AB and ON ⊥ CD

To prove : ∠OMN = ∠ONM

Proof : We know that equal chord of a circle are equidistant from center. 

Thus OM = ON ΔOMN will be an isosceles triangle.

In isosceles triangle angles opposite to equal sides are equal

Thus ∠OMN = ∠ONM