Question

if two equal chords of a circle intersect within the circle prove that the line joining the point of intersection to the centre makes equal angles with the chord​

Answer 1

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