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
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