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 chords.
Let's suppose that we have circle with centre O. There are two equal chords AB and CD intersecting at point E.
Construction: Draw and . Join OE.
We need to prove that
In and , we have
(Each equal to )
(Equal chords are equidistant from the centre)
Therefore, by RHS congruence rule, we have
(Corresponding parts of congruent triangles are equal)