What is the sum of the radii of the circles?
Consider the following for the next three (03) items that follow: ABC is a triangle with sides AB=6\text{ cm}, BC=10\text{ cm} and CA=8\text{ cm}. With vertices A, B and C as centres, three circles are drawn each touching the other two externally.
- A. 10.4 cm
- B. 11.2 cm
- C. 12 cm ✓
- D. 13 cm
Correct Answer: C. 12 cm
Explanation
Let the radii be r_a, r_b, r_c. The distances between centers are the sides of the triangle: r_a+r_b=6, r_b+r_c=10, and r_c+r_a=8. Adding all three equations yields 2(r_a+r_b+r_c) = 24 \implies r_a+r_b+r_c = 12\text{ cm}.
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