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.

• A. $\sqrt{24}cm$
• B. $4\sqrt{6}cm$
• C. $8\sqrt{3}cm$
• D. $4\sqrt{3}cm$

Answer 1

Answer: (B)

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.

$AB=AO-BO=5-3=2cm$ (since AO and BO are radii of larger and smaller circles)

$AC=\frac{AB}{2}=\frac{2}{2}=1cm$

now in right angled triangle AMP

$AC=1cm,AP=5cm$

by pythagoras thm.

${AP}^2={PC}^2+{AC}^2$

${PC}^2=\sqrt{{AP}^2-{AC}^2}$

${PC}^2=\sqrt{5^2-1^2}$

Therefore $PQ=2PC=2.\sqrt{24}=4.\sqrt{6}cm$ [CP=CQ]

So , option A is the answer.