# Three circles are drawn with the vertices of a triangle as centres such that each circle touches the other two. If the sides of the triangle are 2 cm, 3 cm, and 4 cm, find the diameter of the smallest circle.(a) 1 cm(b) 3 cm(c) 5 cm(d) 4 cm. Please give the working also.. Let ABC be the triangle and three circles are drawn such that each circle touches the other two.

Let x be the radius of circle drawn at A. y be the radius of circle drawn at C and z be the radius of the circle drawn at B.

Let the sides

AC = 2 cm

AB = 3 cm

BC = 4 cm

∴ AC = x + y = 2  ........ (1)

AB = x + z = 3  ........ (2)

BC = y + z = 4  ........ (3)

On adding (1), (2) & (3), we get

2 (x + y + z) = 9

x + y + z = 4.5  ...... (4)

Since x + y + z = 4.5

and x + y = 2

z = 4.5 – 2

z = 2.5 cm

y + z = 4

⇒ x = 4.5 – 4

x = 0.5 cm

z + x = 3

y = 1.5 cm

Hence the radius of smallest circle is 0.5 cm

∴ Diameter of the smallest circle is 0.5 × 2 = 1 cm

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ans. is (d)--4 cm

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oh sry i dnt knw d ans of dis ques.???

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i know that the answer is 1 cm... but how...?

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i dnt knw yr??

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