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2. Prove that, if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Answer :

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., \(\angle{MON}\) = \(\angle{PO'Q}\)
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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)