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Question

In the given figure, two circles with centres A and B of radii 5 cm and 3 cm touch each other internally.
If the perpendicular bisector of segment AB meets the bigger circle in P and Q, find the length of PQ.
509253_f2e7ec7c22674e79890a6b6f954673e9.png

A
46cm
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B
24cm
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C
83cm
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D
43cm
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Solution

The correct option is B 46cm



A and B are the centres of the circles with radii 5cm and 3cm respectively.

C is the mid-point of AB.
Extend AB upto O point on circumference of outer circle.
AB=AOBO=53=2cm (since AO and BO are radii of larger and smaller circles)

AC=AB2=22=1cm


now in right angled triangle AMP

AC=1cm,AP=5cm

by pythagoras thm.
AP2=PC2+AC2
PC2=AP2AC2
PC2=5212
Therefore PQ=2PC=2.24=4.6cm [CP=CQ]
So , option A is the answer.

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