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

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

KVPYKVPY 2016

Solution:

Given, radii of circle are $1, 2$ and $3$.

image

$\therefore $ Side of $\Delta ABC$ are

$AB = 5$

$BC=3$

$AC = 4$

$\therefore \Delta ABC$ is formed a right angled triangle where $AB$ is hypotenuse of triangle.

We know circumradius of a right angled triangle is the half of the hypotenuse.

$\therefore $ Circumradius $= \frac{1}{2} \times AB$

$= \frac{1}{2} \times 5 = 2.5$