2021 · Q81
Consider the following for the next three (03) items that follow : ABC is a triangle with sides AB = 6 cm, BC = 10 cm and CA = 8 cm. With vertices A, B and C as centres, three circles are drawn each touching the other two externally. What is the sum of the radii of the circles ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A10.4 cm
- B11.2 cm
- C12 cm
- D13 cm
Explanation
If the radii are r_A, r_B, r_C, external tangency gives r_A + r_B = 6, r_B + r_C = 10, r_C + r_A = 8. Adding: 2(r_A + r_B + r_C) = 24, so the sum of the radii is 12 cm. This is option (c).