Question

7. Two concentric circles of radii 5cm and 3 cm. Find the length of the chord of the larger drcle which touches the smaller circle.
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Answer 1

Given:

• OP = Internal radius = 3 cm
• OB = External radius = 5 cm

To find:

➩ AB = ?

Method:

We know that;

Perpendicular drawn from centre of a circle to the chord bisects the chord.

∴ AP = BP

In ΔOPB,

By Pythagoras theorem,

(OB)² = (OP)² + (BP)²

⇒ (5)² = (3)² + (BP)²

⇒ 25 = 9 + (BP)²

⇒ BP² = 25 - 9

⇒ BP² = 16

⇒ BP = √16

⇒ BP = ± 4

Side cannot be negative.

∴ BP = 4 cm

AB = AP + PB

⇒ AB = 2BP

⇒ AB = 2(4)

∴ AB = 8 cm