Question

In two concentric circles centred at O, a chord AB of the larger circle touches the smaller circle at C. If OA = 3.5 cm, OC = 2.1 cm, then AB is equal to:

Options

• 5.6 cm

• 2.8 cm

• 3.5 cm

• 4.2 cm

Answer 1

5.6 cm

Explanation:

Given OA = 3.5 cm, OC = 2.1 cm

Since OC ⊥ AB

∴ OCA is a right-angle triangle.

By using Pythagoras theorem,

OA² = OC² + AC²

(3.5)² – (2.1)² = AC²

12.25 – 4.41 = AC²

AC² = 7.84

AC = `sqrt(7.84)`

AC = 2.8 cm

AB = 2AC

AB = 2 × 2.8

AB = 5.6 cm