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

Accepted Answer

9. Intercepts of $3x + 5y = 45$: $X$-intercept at $(15,0)$ and $Y$-intercept at $(0,9)$. $T$ is a right-angled triangle at the origin $(0,0)$. Circumradius $L = \frac{	ext{Hypotenuse}}{2} = \frac{\sqrt{15^2 + 9^2}}{2} = \frac{\sqrt{225 + 81}}{2} = \frac{\sqrt{306}}{2} \approx \frac{17.49}{2} = 8.745$. The integer closest to $8.745$ is $9$.

Circumcircle Radius of a Right Triangle

Explanation

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