Q. 474.9( 12 Votes )

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


A. 1.5 cm

B. 2 cm

C. 2.5 cm

D. 3 cm

Answer :

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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