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.
Solution:
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
)
(Common)
(Equal chords are equidistant from the centre)
Therefore, by RHS congruence rule, we have
(Corresponding parts of congruent triangles are equal)
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