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# Recall that two circles are congruent, if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centers.

Given: MN and PO are two equal chords of two congruent circles with centre at O and O'.

To prove: $$\angle{MON}$$ and $$\angle{PO'Q}$$

Proof: In $$\triangle{MON}$$ and $$\triangle{PO'Q}$$, we have,

MO = PO' ...(Radii of congruent circles)
NO = QO' ...(Radii of congruent circles)
and MN = PQ ...(Given)
By SSS criterion, we get,

$$\triangle{MON}$$ $$\displaystyle \cong$$ $$\triangle{PO'Q}$$
Hence, $$\angle{MON}$$ = $$\angle{PO'Q}$$ ...(By CPCT)