CAT 2019 Slot 1 — QA Question 8
TrianglesEasy
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
Answer & solution
Answer: 9
Solution
3x + 5y − 45 = 0 cuts the coordinate axes at C(15,0) and A(0,9) as shown in the image below.
∠ABC = 90°, so we can deduce that AC is the diameter of the circumcircle.
[In a right triangle, hypotenuese is the diameter of circumcircle.]
Diameter = √(152 + 92) = √306.
Radius = (√306)/2 = 8.74 ≈ 9 units.
Hence, 9.