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Question

A straight line is drawn curring two equal circles and passing through M the midpoint of the line joining the centres O and O'. Chord AB is equal to chord CD


A

True

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B

False

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Solution

The correct option is A

True


Draw OP AB and O'Q CD

In MOP and MO'Q

OMP = O'MQ (vertically opposite angles)

OPM = O'QM = 90o

OM = O'M (given)

Hence the two triangles are congruent by AAS criteria

OP = O'Q (cpct)

Chords that are equidistant from the centre are equal in length - Hence AB = CD


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