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If two equal chords of a circle intersect within the circle prove that the line joining the point of intersection to the center makes equal angles withe the chord.
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If two equal chords of a circle intersect within the circle prove that...
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}
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If two equal chords of a circle intersect within the circle prove that the line joining the point of intersection to the center makes equal angles withe the chord. Related: Angles Related to a Circle - Mathematics, Class 9
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