2020 · Q71
Two circles touch internally. The sum of their areas is 136π cm² and distance between their centres is 4 cm. What are the radii of the circles?
Elementary MathematicsCircles
- A11 cm, 7 cm
- B10 cm, 6 cm
- C9 cm, 5 cm
- D8 cm, 4 cm
Explanation
R − r = 4 and π(R² + r²) = 136π, so R² + r² = 136. Then (R + r)² = 136 + 2Rr = 136 + (136 − 16) = 256, giving R + r = 16. Solving with R − r = 4 yields R = 10, r = 6.