Q187 / 270 · NDA 2021 (Phase 2) · Mathematics

A circle is passing through the points $(5,-8),(-2,9)$ and $(2,1)$. If $r$ is the radius of the circle, then which one of the following is correct?

  • A
    $r \lt 10$
  • B
    $10 \lt r \lt 30$
  • C
    $30 \lt r \lt 60$
  • Correct answer
    D
    $r \gt 60$

Solution

$\begin{aligned} & \text { Radius }=(5+58)^2+(-8+24)^2=r^2 \\ & \Rightarrow 3569+256=r^2 \\ & \Rightarrow r^2=4225 \\ & \Rightarrow r=\sqrt{4225}=65\end{aligned}$

Hence, the correct answer is option: 'D'.

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