# CAT 2018 Quant Questions

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?

 24, 10 25, 9 24, 12 25, 10

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?

We know that AC is the diameter and $\angle$ ABC = 90°. AC = 2*13 = 26 cm

In right angle triangle ABC,

$AC^2 = AB^2 + BC^2$

$\Rightarrow$ $AB^2+BC^2=26^2$

$\Rightarrow$ $AB^2+BC^2=676$

Let us check with the options.

Option (A): $24^2+10^2 = 676$. Hence, this is a possible answer.

Option (B): $25^2+9^2 = 706 \neq 676$. Hence, this is an incorrect pair.

Option (C): $25^2+10^2 = 725 \neq 676$. Hence, this is an incorrect pair.

Option (D): $24^2+12^2 = 720 \neq 676$. Hence, this is an incorrect pair.

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