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The line $\text{AB}$ is $6$ metres in length and is tangent to the inner one of the two concentric circles at point $\text{C}.$ It is known that the radii of the two circles are integers. The radius of the outer circle is

1. $5$ metres
2. $4$ metres
3. $6$ metres
4. $3$ metres

Important steps to solve this question:

1. The perpendicular from center (O) to C will divide the chord AB into equal halves. Hence BC = AC = 3 metres.
2. Now, in △ OCB, ∠ OCB = 90°. Hence the sides of this triangle will obey the Pythagorean rule. Hence, OB² = OC² + BC²
3. If BC is 3 metres, the only possible Pythagorean triplet would be 3, 4 and 5. Hence OB = 5 metres.
28 points

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