CAT 2021 Slot 1 QA Question 6: A circle of diameter 8 inches is inscribed in a triangle ABC where $\angle ABC = 90^\circ$. If $BC = 10$ inches then the area of the triangle in square inches is

Question

A circle of diameter 8 inches is inscribed in a triangle ABC where $\angle ABC = 90^\circ$. If $BC = 10$ inches then the area of the triangle in square inches is

Accepted Answer

Let $AB = x$. Since the circle has diameter 8, the inradius of the right triangle is 4.
For a right triangle, the inradius is half of the sum of the two legs minus the hypotenuse.
$4 = \dfrac{x + 10 - \sqrt{x^2 + 100}}{2}$
$\sqrt{x^2 + 100} = x + 2$
$x^2 + 100 = (x + 2)^2$
$x = 24$
Therefore, the ar

A circle of diameter 8 inches is inscribed in a triangle ABC where ∠ABC=90∘\angle ABC = 90^\circ∠ABC=90∘. If BC=10BC = 10BC=10 inches then the area of the triangle in square inches is

A circle of diameter 8 inches is inscribed in a triangle ABC where $\angle ABC = 90^\circ$ . If $BC = 10$ inches then the area of the triangle in square inches is