Question

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​

Answer 1

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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