Question

Three circles have the centres at A, B, C and each circle touches the other two externally. If AB = 5 cm, BC = 7 cm, and CA = 6 cm, then the radii of three circles respectively are

• A. 2, 3, 4
• B. 3, 4, 5
• C. 2, 4, 5
• D. 2, 3, 5

Answer 1

The correct option is A 2, 3, 4

Let p, q, r be radius of 3 circles (see the diagram)

$\Rightarrow p+q=5$ $\to$equation (1)

$\Rightarrow q+r=7$ $\to$equation (2)

$\Rightarrow r+p=6$ $\to$equation (3)

Equation (1)-(2);

$\Rightarrow r-p=2$ $\to$equation (4)

Equation (4)+(3);

$\Rightarrow 2r=8\Rightarrow r=4$

Substituting in equation (2) we get $q=3$

Substituting in equation (1) we get $p=2$

$\therefore$ The radius of 3 circles are 2,3,4