Question

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 to the chords.​

Answer 1

Step-by-step explanation:

In △OMX and △ONX,

∠OMX=∠ONX=90

∘

OX=OX(common)

OM=ON where AB and CD are equal chords and equal chords are equidistant from the centre.

△OMX≅△ONX by RHS congruence rule.

∴∠OXM=∠OXN

i.e.,∠OXA=∠OXD

Hence proved.