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Question
Prove that equal chords of congruent circles subtend equal angles at their center.
Solution
Given: AB and CD are two equal chords of a congruent circle with centres O and O respectively.
To prove: ∠AOB = ∠CO'D
Proof:
In ΔOAB and ΔO'CD
OA = O'C ...[ ∵ Radii of congruent circles ]
OB = O'D ...[ ∵ Radii of congruent circles ]
AB = CD ...[ Given ]
ΔOAB ≅ ΔO'CD ...[ By SSS congruence criterion ]
∠AOB = ∠CO'D ...[ c. p. c. t ]
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