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.`

Explanation

In the given figure, we have,

`(AP)^2 = ((PQ)/2)^2+((AB)/2)^2`->(1)

Here, `AP =` Radius of large circle`(R) = 5` cm

`AB = `Difference of both radius `= 5-3 = 2` cm

Putting these values in (1),

`25 = ((PQ)/2)^2+1`

`PQ^2 = 24**4=> PQ = sqrt96 = 4sqrt6` cm

So, length of `PQ` is `4sqrt6` cm.