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The line AB is $6$ metres in length and is tangent to the inner one of the two concentric circles at point 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 

 

in Logical Reasoning 7.8k points 162 792 1071 320 views

1 Answer

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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 1 1 2

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