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18/07/2021 11:26 am
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Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
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18/07/2021 11:28 am
Consider the following diagram
Here, it is given that AOB = COD i.e. they are equal angles.
Now, we will have to prove that the line segments AB and CD are equal i.e. AB = CD.
Proof:
In triangles AOB and COD,
AOB = COD (as given in the question)
OA = OC and OB = OD (these are the radii of the circle)
So, by SAS congruency, ΔAOB ΔCOD.
∴ By the rule of CPCT, we have
AB = CD. (Hence proved).