Question

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.

Answer 1

Let the radii of the circles with A, B and C as centres be r1, r2 and r3 respectively.

According to the given information,

AB = 10 cm = r1 + r2 … (1)

BC = 8 cm = r2 + r3 … (2)

CA = 6 cm = r1 + r3 … (3)

Adding equations (1), (2) and (3),

2(r1 + r2 + r3) = 24

r1 + r2 + r3 = 12 … (4)

Subtracting (1) from (4),

r3 = 12 – 10 = 2

Subtracting (2) from (4),

r1 = 12 – 8 = 4

Subtracting (3) from (4),

r2 = 12 – 6 = 6

Thus, the radii of the three circles are 2 cm, 4 cm and 6 cm.