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.
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.
Updated On: Aug 22, 2024
- 10 cm, 6 cm and 2 cm
- 2 cm, 5 cm and 3 cm
- 6 cm, 8 cm and 9 cm
- 12 cm, 10 cm and 5 cm
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The Correct Option is A
Solution and Explanation
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.
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.
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