2021 · Q15
The sides of a triangle ABC are 4 cm, 6 cm, and 8 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?
Elementary MathematicsCircles
- A6 cm
- B7 cm
- C9 cm
- D10 cm
Explanation
Let the radii be r₁, r₂, r₃ at vertices A, B, C. Then r₁ + r₂ = 4, r₂ + r₃ = 6, r₃ + r₁ = 8. Adding all three: 2(r₁ + r₂ + r₃) = 18, so the sum of the radii is 9 cm. Hence option C.