Question

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

• A. 1.5
• B. 2
• C. 2.5
• D. 3

Answer 1

Answer: (C)

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



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

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