2. Prove that, if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Given: MW and PQ are two chords of congruent circles such that angles subtended by these chords at the centres O and O' of the circles are equal i.e., $$\angle{MON}$$ = $$\angle{PO'Q}$$
Proof: In $$\triangle{MON}$$ and $$\triangle{PO'Q}$$, we have,
and $$\angle{MON}$$ = $$\angle{PO'Q}$$ ...(Given)
$$\triangle{MON}$$ $$\displaystyle \cong$$ $$\triangle{PO'Q}$$