In the figure, two circles with centres `A and B` and of radii `5cm and 3cm` touch each other intermally. If the perpendicular bisectors of segment AB meets the bigger circle in `P and Q.` Find the length of `PQ.`

In the figure, two circles with centres `A and B` and of radii `5cm an

1.	In the figure, two circles with centres `A and B` and of radii `5cm and 3cm` touch each other intermally. If the perpendicular bisectors of segment AB meets the bigger circle in `P and Q.` Find the length of `PQ.`
Answer» Here, AM=5cm,BM=3cm. `thereforeAB=AM-BM=5-3=2cm` It is also given that PQ is the perpendicular bisector of AB. `therefore AC=CB=(1)/(2)AB=1cm` and `anglePCA=90^@` Now, in right triangle PCA, `PC^2=AP^2-AC^2` (by Pythagoras theorem) `=(5)^2-(1)^2=24` `therefore PC =sqrt(24)cm` `rArrPC=2(sqrt6)cm` `therefore PQ=2PC` (because perpendicular drawn from the centre to the chord bisects the chord `=2xx2sqrt(6)cm` `rArrPQ=4sqrt(6)cm`.

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In the figure, two circles with centres `A and B` and of radii `5cm and 3cm` touch each other intermally. If the perpendicular bisectors of segment AB meets the bigger circle in `P and Q.` Find the length of `PQ.`

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