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CAT 2018 [SLOT 1] Quant Question with Solution 22

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?

1. 24, 10
2. 25, 9
3. 24, 12
4. 25, 10

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): $24^2+10^2 = 676$.

Option (B): $25^2+9^2 = 706 \neq 676$.

Option (C): $25^2+10^2 = 725 \neq 676$.

Option (D): $24^2+12^2 = 720 \neq 676$.

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