Radius of larger circle = 5 cm.
Radius of smaller circle = 3 cm.
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
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
AB = 2 AP
= 2(4) = 8 cm
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