cat 2023 Question 18

Question

A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a:b . If the radius of the circle is r , then the area of the triangle is

Accepted Answer

Since BC is the diameter of the circle, which implies angle BAC is 90 degrees. Let AB = a cm, which implies AC = b cm. Hence, $ BC = \sqrt{a^2 + b^2} $, which is diameter of the circle (2r).

Hence, $ 2r = \sqrt{a^2 + b^2} $

=> $ 4r^2 = a^2 + b^2 $

The area of the triangle is $ \frac{1}{2} imes a imes b $, which can be written as

=> $ \frac{a \cdot b}{2(a^2+b^2)} imes (a^2 + b^2) $

=> $ \frac{a \cdot b}{2(a^2+b^2)} imes 4r^2 $

=> $ \frac{a \cdot b}{a^2+b^2} imes 2r^2 $

The correct option is D

Question 18.

Question Explanation