CAT 2019 Quant Question with Solution 14

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

Clearly, the triangle will be right angled triangle and the hypotenuse would be the diameter of the circumcircle.

Getting the coordinates by substituting x and y with 0 alternatively in the equation 3x+5y-45=0,  we have

Hypotenuse = $\sqrt{{{9}^{2}}+{{15}^{2}}}=\sqrt{306}\approx 17.5$

Therefore, the radius =$\frac{17.5}{2}\approx 8.7$

Hence, the closest integer = 9.

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