Question

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

• A. 2.5
• B. 7
• C. 8.4
• D. 1.7

Answer 1

Answer: (A)

2.5

$C_1\equiv r\Rightarrow 1$

$C_2\equiv r\Rightarrow 2$

$C_3\equiv r\Rightarrow 3$

Therefore after we join the centres we'll get a right angle triangle of sides $3,4$ and $5$

$\therefore d=\frac{abc}{2\times Area}$

$\Rightarrow d=\frac{3\times 4\times 5}{2\times 6}=5$

$r=\frac{d}{2}=2.5units$