Two circles of radii 13 cm and 10 cm intersect at the points P and Q.  If PQ = 10 cm and the distance between the centers of the circle is x cm, the value of x is?

20.5

In ΔPOM

⇒ directly use triplet (5, 12, 13) ⇒ OM = 12

and

In ΔPON,

Using pythagoras theorem :

⇒ ON = \(\sqrt {10^2 - 5^2}\) = 5\(\sqrt {3}\)

Hence, MN = 12 + 5\(\sqrt {3}\) = 20.5 cm