Three circles of radii 1, 2 and 3 units respe | vedclass

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(C) Let the centers of the circles be $A, B$ and $C$ with radii $r_1 = 3, r_2 = 2$ and $r_3 = 1$ respectively.Since the circles touch each other exter

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$2.5$

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(C) Let the centers of the circles be $A, B$ and $C$ with radii $r_1 = 3, r_2 = 2$ and $r_3 = 1$ respectively.Since the circles touch each other externally,the distances between the centers are the sum of their radii:$AB = r_1 + r_2 = 3 + 2 = 5$$BC = r_2 + r_3 = 2 + 1 = 3$$AC = r_1 + r_3 = 3 + 1 = 4$In $	riangle ABC$,we observe that $AB^2 = 5^2 = 25$ and $BC^2 + AC^2 = 3^2 + 4^2 = 9 + 16 = 25$.Since $AB^2 = BC^2 + AC^2$,$	riangle ABC$ is a right-angled triangle with the hypotenuse $AB = 5$.The circumradius $R$ of a right-angled triangle is half of its hypotenuse.$R = \frac{AB}{2} = \frac{5}{2} = 2.5$ units.

Three circles of radii $1, 2$ and $3$ units respectively touch each other externally in the plane. The circumradius of the triangle formed by joining the centers of the circles is

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