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Choose whether the given statement is true or false.

If chords of congruent circles subtend equal angles at their centers, then the chords are equal.

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True

False

answer is A.

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Detailed Solution

Since, the circles are congruent i.e., the radii of both the circles will be equal
Let us consider two circles with centres O and O’

∆ OAB

and

∆ O' CD

OA = O’C (radii of congruent circles)
OB = O’D (radii of congruent circles)

∠ AOB = ∠ CO' D

(given)
By SSS congruence,

∆ OAB

≅

∆ O' CD

AB = CD (by CPCT)
Thus, chords of both the circles are equal.
Hence, the given statement is true.

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