CAT 2021 Slot 1 · Quant · Question 10
CAT 2021 Slot 1 previous year question on Triangles, with the answer and a step-by-step solution.
A circle of diameter 8 inches is inscribed in a triangle ABC where \angle ABC={90}^{∘}. If BC=10 inches then the area of the triangle in square inches is
Answer & solution
Answer: 120
The inradius is r=4.
For a right triangle, r=\frac{AB+BC-AC}{2}.
Writing AB=y and AC=c, \frac{y+10-c}{2}=4 gives c=y+2.
Also {c}^{2}={10}^{2}+{y}^{2},
so {\left( y+2 \right)}^{2}=100+{y}^{2},
giving 4y=96 and y=24.
Hence the area is \frac{1}{2}\times 10\times 24=120.
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