CAT 2018 Question Paper Shift 1 Solved Paper

Question : 82 of 100

Marks: +1, -0

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?
Options

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

Validate

Solution:

We know that AC is the diameter and

∠ {ABC}=90^{∘} . {AC}=2{*} 13=26 {cm}

In right angle triangle ABC

A C^{2}=A B^{2}+B C^{2}

⇒ A B^{2}+B C^{2}=26^{2}

⇒ A B^{2}+B C^{2}=676

Let us check with the options.
Option (A):

24^{2}+10^{2}=676

Option (B):

25^{2}+9^{2}=706 ≠ 676

Option

(C): 25^{2}+10^{2}=725 ≠ 676

Option (D):

24^{2}+12^{2}=720 ≠ 676

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