Draw that Two circles Are congruent If they have the small radii . prove that Equal Chords Of congruent circles Subtend Equal Angles At their Centre...
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Step-by-step explanation:
This is same as the previous question. The theorem says that if two chords subtend equal angles at centre then the chords are equal. Hence, if two chords in two congruent circles subtend equal angles at their centres then the chords are equal.
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Answer:
Given : Two congruent circles with centres O and O' and radii r which have chords AB and CD respectively such that AB = CD.
To Prove : ∠AOB = ∠CO'D
Proof : In ∠AOB and ∠CO'D, we have
AB = CD [Given]
OA = O'C [Each equal to r]
OB = O'D [Each equal to r]
∴ ∆AOB ≅ ∆CO'D [By SSS congruence criteria]
⇒ ∠AOB = ∠CO'D [C.P.C.T.]
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