Question

Ir 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 chords.
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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.