In the given figure, three circles with centers A, B, C respectively touch each other externally.

If AB = 5 cm, BC = 7 cm and CA = 6 cm then the radius of the circle with center A is

In the given Figure

AR = AP = x(let) [Radii of same circle]

BP = BQ = y(let) [Radii of same circle]

CR = CQ = z(let) [Radii of same circle]

Now,

AB = 5 cm [Given]

AP + BP = 5

x + y = 5

y = 5 - x …[1]

BC = 7 cm [Given]

BQ + CQ = 7

y + z = 7

5 - x + z = 7 [using 1]

z = 2 + x …[2]

and

AC = 6 cm [Given]

x + z = 6

x + 2 + x = 6 [Using 2]

2x = 4

x = 2 cm