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Concentric Circles Tangent

CAT 1993 Slot 1 · Quantitative Ability · Medium · QA

This is a medium Quantitative Ability question from the CAT 1993 Slot 1 paper. It tests QA. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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The line ABAB is 66 metres in length and is tangent to the inner one of the two concentric circles at point CC. It is known that the radii of the two circles are integers. The radius of the outer circle is

  1. A.

    5 metres

  2. B.

    4 metres

  3. C.

    6 metres

  4. D.

    3 metres

Answer

A

Explanation

Let RR and rr be the radii of the outer and inner circles respectively. CC is the midpoint of ABAB, so CB=3CB = 3 metres. In △OCB\triangle OCB, R2−r2=CB2=9R^2 - r^2 = CB^2 = 9. Thus (R−r)(R+r)=9×1(R-r)(R+r) = 9 \times 1. Since RR and rr are integers, R+r=9R+r = 9 and R−r=1R-r = 1, giving R=5R = 5 metres.

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