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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 cm
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 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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