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CAT 2021 Slot 1 QA Question & Solution

GeometryMedium

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

Solution

Question Figure

We know that Inradius=$\frac{\left(Perpendicular+Base-Hypotenuse\right)}{2}$

$4=\frac{\left(p+10-h\right)}{2}$

h-p = 2 or h= p+2.

Now, $p^2+100\ =\ h^2$

$p^2+100\ =\ \left(p+2\right)^2$

$p^2+100\ =\ p^2+4p+4$

4p = 96

p=24.

Hence, Area = $\frac{1}{2}\times\ 10\times\ 24\ =\ 120$.