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Question

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

A
25 cm
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B
28 cm
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C
30 cm
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D
52 cm
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Solution

## The correct option is B 28 cmThe 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 to Δ OAC, 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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