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Rectangle Inscribed in Circle

CAT 2019 Slot 1 · Quantitative Ability · Easy · Geometry

This is an easy Quantitative Ability question from the CAT 2019 Slot 1 paper. It tests Geometry. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?

  1. A.

    25, 10

  2. B.

    24, 12

  3. C.

    25, 9

  4. D.

    24, 10

Answer

D

Explanation

For a rectangle inscribed in a circle of radius R=13R = 13, the diagonal is the diameter D=26D = 26. If length is LL and breadth is BB, then L2+B2=D2=262=676L^2 + B^2 = D^2 = 26^2 = 676. Testing options: (D) 242+102=576+100=67624^2 + 10^2 = 576 + 100 = 676. Perfect match.

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