Q5 of 63 Page 145

In figure, AB and CD are equal chords of a circle. O is the centre of the circle of OM ⊥ AB and ON ⊥ CD. Then prove that ∠OMN = ∠ONM.

Given AB and CD are equal chords of a circle with centre O.


Also OM ⊥ AB and ON ⊥ CD.


We have to prove that ∠OMN = ∠ONM.


Proof:


We know that equal chords of a circle are equidistant from the centre.


⇒ OM = ON … (1)


In ΔOMN,


From (1),


⇒ OM = ON


We know that angles opposite to equal sides of a triangle are equal.


∴ ∠OMN = ∠ONM


Hence proved.


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