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

AB = 10 cm,
BC = 8 cm and
AC = 6 cm

Let the radii of three circle be r1, r2 and r3   ...(Shown in fig.)
r₁ + r₂ = 10 = AB       ....(1)
r₂ + r₃ = 6 = AC         ....(2)
r₃ + r₁ = 8 = BC         .....(3)

Adding (1), (2) and (3), we get
2 (r₁ + r₂ + r₃ ) = 10 + 6 + 8 = 24
r₁ + r₂ + r₃  = 12        .....(4)

Subtract (4) and (1) ⇒ r₃  = 12 - 10 = 2 cm

Subtract (4) and (2) ⇒ r₁  = 12 - 6 = 6 cm

Subtract (4) and (3) ⇒ r₂  = 12 - 8 = 4 cm