Q) Two concentric circle are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.


Two concentric circle are CBSE board PYQ

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 = 5 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)

\therefore AP = PB

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

OB2 = OP2 + PB2

(5) 2 = (3) 2 + PB2

PB2 = 16

or PB = 4

Since AP = PB or we can say, AB = 2 PB

Hence, AB = 8 cm

Therefore, length of the chord of larger circle is 8 cm.

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