Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Solution:
We have two congruent circles with centres O and O’ respectively. They are congruent which means that they have same radii.
It is also given that
We need to prove that
.
In
and
, we have
(Congruent circles have same radii)
(Given)
(Congruent circles have same radii)
Therefore, by SAS congruence rule, we have
.
(Corresponding parts of congruent triangles are equal.)
It means that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
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