# 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., $$\angle{MON}$$ = $$\angle{PO'Q}$$

To prove: MN = PQ

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

MO = PO' ...(Radii of congruent circles)
NO = QO' ...(Radii of congruent circles)
and $$\angle{MON}$$ = $$\angle{PO'Q}$$ ...(Given)
By SAS criterion, we get,

$$\triangle{MON}$$ $$\displaystyle \cong$$ $$\triangle{PO'Q}$$

Hence, MN = PQ ...(By CPCT)