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

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)

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