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CAT 2019 Slot 1 QA Question & Solution

GeometryHard

Question

Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is

Solution

Question Figure

In any right triangle, the circumradius is half of the hypotenuse. Here,$L = \frac{1}{2} \times \text{ the length of the hypotenuse} = \frac{1}{2}(\sqrt{15^2+9^2}) = \frac{1}{2} \times \sqrt{306} \approx \frac{1}{2} \times 17.49 = 8.74$

Hence, the integer close to L = 9