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Q.

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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a

True

b

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’
   Question Image In ∆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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