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

The radii of circles with centres A, B and C are $x$, $y$ and $z$ respectively.

x + y = 7...........(i)

y + z = 8..........(ii)

z + x = 5.......(iii)

Subtracting (i) and (ii) we get

z - x = 1......(iv)

Adding (iii) and (iv) we get

2z = 6 $\Rightarrow$ z = 3 cm.

Substituting z = 3 in (iv),

x = 2 cm.

substituting x = 2 in (i),

y = 5 cm.