Question

In the figure chord AB= chord CD. seg OM is perpendicular to chord CD, then prove angle OMN = angle ONM.​

Answer 1

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Hey Mate!!

Given,

AB = CD

OM ⊥ AB

ON ⊥ CD

Two equal chords of a circle are equidistant from the center of the circle.

⇒ OM = ON

In ΔMON,

MO = ON ⇒ ΔMON is isosceles.

→ ∠OMN = ∠ONM  (∵Angles opposite to equal sides of isosceles Δ)

Answer 2

Answer:

Hey Mate!!

Given,

AB = CD

OM ⊥ AB

ON ⊥ CD

Two equal chords of a circle are equidistant from the center of the circle.

⇒ OM = ON

In ΔMON,

MO = ON ⇒ ΔMON is isosceles.

→ ∠OMN = ∠ONM (∵Angles opposite to equal sides of isosceles Δ)