1. 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)