Two circles with centers A and B, and radii 5 cm and 3 cm, touch each other internally. If the perpendicular bisector of the segment AB meets the bigger circle in P and Q; find the length of PQ.

We know that,

If two circles touch internally, then distance between their centres is equal to the difference of their radii. So,

   

Also, the common chord

   

is the perpendicular bisector of

   

Thus,

   

In right 

   

we have

   

[Pythagoras Theorem]

   

Or,

   

   

Now,

   

   

So,

   

Therefore, the length of