Question

Three circles with centers at ‘A’, ‘B’ and ‘C’ touches each other externally as shown in the figure. If AB = 16cm, BC = 8 cm and AC = 12 cm, then find the radii of all three circles.

• A. 10 cm, 6 cm and 2 cm
• B. 2 cm, 5 cm and 3 cm
• C. 6 cm, 8 cm and 9 cm
• D. 12 cm, 10 cm and 5 cm

Answer 1

The Correct Option is A

Let ‘r1, ‘r₂ and ‘r₃ be the radii of the circles with centre at ‘A’, ‘B’ and ‘C’, respectively.
So, r₁ + r₂= 16 …… (1)
r₂ + r₃ = 8 …… (2)
r₁ + r₃ = 12 …… (3)
Adding equations (1), (2) and (3)
2 × (r₁ + r₂ + r₃) = 36
Or, r₁ + r₂ + r₃ = 18
Therefore, r₁ = 18 - 8 = 10
And, r₂ = 18 - 12 = 6
And, r₃ = 18 - 16 = 2 cm
So, the correct option is (A) : 10 cm, 6 cm and 2 cm.