Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour
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)