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.

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Solution

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.

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