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Question

# The length of common chord of two intersecting circles is 30 cm. If the diameters of these two circles be 50 cm & 34 cm, the distance between their centres is ____ cm.

A

30

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B
28
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C
24
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D
32
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Solution

## The correct option is B 28 The perpendicular drawn from centre of the circle bisects the chord. OO' bisects the chord AB into two equal parts of 15 cm each. AC = CB = 15cm Now applying Pythagoras Theorem in ΔOAC we get, (25)2 = (15)2 + (X)2 625 = 225 + (X)2 X = 20 cm Now Applying Pythagoras Theorem in ΔO'AC we get, (17)2 = (15)2 + (Y)2 289 = 225 + (Y)2 Y = 8 cm Therefore distance between the two centres is (X + Y) = (20 + 8) = 28 cm.

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