2025 · Q12
C is the centre of a circle of radius 20 cm. AB is a chord of length 32 cm. E is a point on AB such that CE = 13 cm. What is AE × EB equal to?
Elementary MathematicsCircles
- A231 square cm
- B256 square cm
- C272 square cm
- D297 square cm
Explanation
The midpoint D of chord AB (length 32) satisfies AD = 16, and CD = √(20² − 16²) = 12. For E on AB with CE = 13, DE = √(CE² − CD²) = √(169 − 144) = 5. Hence AE = 16 + 5 = 21 and EB = 16 − 5 = 11 (or vice versa), so AE × EB = 21 × 11 = 231, option (a).