CAT 2018 Slot 1 QA Question 28: 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?

Question

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?

Accepted Answer

The diagonal of a rectangle inscribed in a circle is the diameter of the circle.
Diameter $=2 	imes 13 = 26$ cm.
So, length and breadth must satisfy
$l^{2} + b^{2} = 26^{2} = 676$
Checking the options:
$24^{2} + 10^{2} = 576 + 100 = 676$
Hence, 24 cm and 10 cm are possible.