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?

Given:

C is the center of a circle with radius = 20 cm.

AB is a chord of length = 32 cm.

CE = 13 cm, E is a point on AB.

We need to find AE × EB.

Formula used:

In a circle, for any chord AB and point E on AB:

AE × EB = (Radius² - Distance from center to chord²)

Calculation:

Radius = 20 cm, so Radius² = 20² = 400

Distance from center to chord (CE) = 13 cm, so CE² = 13² = 169

⇒ AE × EB = Radius² - CE²

⇒ AE × EB = 400 - 169

⇒ AE × EB = 231

∴ The correct answer is option (1).