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The given fig...

Question

The given figure shows two circles with centres A and B; and radii 5 cm and 3 cm respectively, touching each other internally. If the perpendicular bisector of AB meets the bigger circle in P and Q, find the length of PQ.

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Solution

$AB = AC - BC = 5 - 3 = 2 \ cm$

$PQ$ bisects $AB$ (let the point be $R$ )

$AR = 1 \ cm$

In $\triangle APR$

$AP^2= RP^2+AR^2$

$\Rightarrow 25 = RP^2+1 \Rightarrow RP = 24 = 2\sqrt{6} \ cm$

$\\$

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