Question

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

• A. $1.5$
• B. $2$
• C. $2.5$
• D. $3$

Answer 1

The correct option is C $2.5$

If you draw the diagram after joining the centres you will get a right angled triangle of sides 3,4, and 5 units lengths.

This is because $5^2=3^2+4^2$

So, by converse of Pythagoras theorem, Angle formed at the intersection of sides of lengths 3 and 4 units is right angle.

Diameter of any circle subtends a right angle at points on its circumference.

So, here, side of length 5 units will be the diameter.

So, $Radius=\frac{1}{2}Diameter=2.5$ units.

option C is the answer.