CAT 2019 Shift 1 Paper

Question : 81 of 100

Marks: +1, -0

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

Your Answer:

Validate

Solution:

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

3 x+5 y-45=0,

we have

Hypotenuse

=√{9^{2}+15^{2}}=√{306} ≈ 17.5

Therefore, the radius

=\;{17.5}/{2} ≈ 8.7

Hence, the closest integer

=9 .

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