Question

In the figure given below AB = 7 cm BC = 8 cm CA = 5 cm. What are the radii of the circles A, B and C?

• A. 2 cm, 4 cm and 5 cm
• B. 1 cm, 3 cm and 7 cm
• C. 2 cm, 5 cm and 3 cm
• D. 1 cm, 3 cm and 4 cm

Answer 1

The correct option is C

2 cm, 5 cm and 3 cm

AB is nothing but sum of radii of circle A and circle B. Likewise for BC and CA.

Let's try forming three simultaneous equations.

The radii of circles with centres A, B and C are $x$, $y$ and $z$ respectively.
$x+y=7$, $y+z=8$, $z+x=5$
$\Rightarrow y=8-z$, Putting this value in $x+y=7$
$\Rightarrow x+8-z=7$
$\Rightarrow x-z=-1$
Also, $x+z=5$
Solving for x, y and z, we get x = 2 cm, y = 5 cm and z = 3 cm