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?

By the intersecting chord property (power of a point), AE × EB = r² − CE² when the perpendicular from centre is considered. Actually, AE × EB = (radius² − distance from centre to chord²) doesn't directly apply; use: if M is midpoint of AB, CM ⊥ AB and CM = √(20² − 16²) = √(400−256) = √144 = 12. Then EM = √(CE² − CM²) = √(169 − 144) = √25 = 5. So AE = 16 − 5 = 11 (or 16 + 5 = 21) and EB = 16 + 5 = 21 (or 16 − 5 = 11). AE × EB = 11 × 21 = 231.