# Two concentric ci

Given:

Radius of larger circle = 5 cm.

Radius of smaller circle = 3 cm.

Solution:

The diagram for the question is as follows:

AB is a tangent for smaller circle, and we know that tangent at any point is perpendicular to the radius through point of contact.

Hence, OP AB

Also, AB is a chord for large circle, and we know perpendicular from center to the chord bisects the chord

Hence,

Now, In ΔOAP

By Pythagoras theorem,

OA2 = AP2 + OP2

AP2 = OA2 – OP2

Here, OA = radius of bigger circle = 5 cm

and OB = radius of smaller circle = 3 cm

AP2 = 52 – 32

AP2 = 25 – 9

AP2 = 16

AP = 4 cm

Hence,

AB = 2 AP

= 2(4) = 8 cm

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