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Question

In the diagram two equal circles of radius 4 em intersect each other such that each passes through the centre of the other. Find the length of the common chord
371050_a157ae560ae24874b8a1f6571a287123.png

A
23cm
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B
43cm
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C
42cm
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D
8 cm
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Solution

The correct option is B 43cm
If O and O be the centres then OO will be the common radius
OO=4cm
OA=OB=OA=OB
(because these are radii)
OAOB is a rhombus.
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But the diagonals of a rhombus intersect each other at right angle
AEO=90
AE2+OE2=AO2
OR, AE2+4=16
AE=12=23
AB=2×23=43cm
484187_371050_ans_b61731abf0324c3082185396cf53a825.png

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