Q) Two concentric circle are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Ans:

Let’s draw a diagram with 2 concentric circles, both having O as centre. Let the radius of two circles be shown as OP = 3 cm of smaller circle and OB = 4 cm for larger circle. Here, AB is the chord of larger circle and it is also tangent of smaller circle.

By circle’s identity, we know that:

a) A radius drawn on a tangent is perpendicular (holds valid for smaller circle)

b) A perpendicular line drawn on a chord bisects it (holds valid for larger circle)

∴ AP = PB

Next, let’s take right angled triangle Δ OPB,

OB² = OP² + PB²

∴ (4) ² = (3) ² + PB²

∴ PB² = 7

∴ PB = √ 7

Since AB = AP + PB

∴ AB = 2 PB = 2 √ 7

Therefore, length of the chord of larger circle is 2√7 cm.

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