The sides of a triangle ABC are 4~\text{cm}, 6~\text{cm} and 8~\text{cm}. With the vertices of the triangle as centres, three circles are drawn each touching the other two externally. What is the sum of the radii of the three circles?
- A. 6 cm
- B. 7 cm
- C. 9 cm ✓
- D. 10 cm
Correct Answer: C. 9 cm
Explanation
Let the radii of the three circles be r_1, r_2, and r_3. The distance between their centers are the sides of the triangle, so r_1+r_2=4, r_2+r_3=6, and r_3+r_1=8. Adding these gives 2(r_1+r_2+r_3) = 18 \implies r_1+r_2+r_3 = 9~\text{cm}.
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