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.
To prove: $$\angle{MON}$$ and $$\angle{PO'Q}$$
Proof: In $$\triangle{MON}$$ and $$\triangle{PO'Q}$$, we have,
$$\triangle{MON}$$ $$\displaystyle \cong$$ $$\triangle{PO'Q}$$
Hence, $$\angle{MON}$$ = $$\angle{PO'Q}$$ ...(By CPCT)