if two equal chords of a circle intersect within the circle prove that the segament of one cord are equal to corresponding segments of another chord
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if two equal chords of a circle intersect within the circle prove that the segament of one cord are equal to corresponding segments of another chord
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Step-by-step explanation:
Let AB and CD are the two equal chords of a circle having center O
Again let AB and CD intersect each other at a point M.
Now, draw OP perpendicular AB and OQ perpendicular CD
From the figure,
In ΔOPM and ΔOQM,
OP = OQ {equal chords are equally distant from the cntre}
∠OPM = ∠OQM
OM = OM {common}
By SAS congruence criterion,
ΔOPM ≅ ΔOQM
So, ∠OMA = ∠OMD
or ∠OMP = ∠OMQ {by CPCT}
Thus, the line joining the point of intersection to the center makes equal angles with the chords.
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