MCQ
Let $C$ be a circle passing through the points $A (2,-1)$ and $B (3,4)$. The line segment $AB$ is not a diameter of $C$. If $r$ is the radius of $C$ and its centre lies on the circle $(x-5)^{2}+(y-1)^{2}=\frac{13}{2}$, then $r^{2}$ is equal to
  • A
    $32$
  • $\frac{65}{2}$
  • C
    $\frac{61}{2}$
  • D
    $30$

Answer

Correct option: B.
$\frac{65}{2}$
b
$AB =\sqrt{26}$

$r ^{2}= CM ^{2}+ AM ^{2}$

$=\left(2 \times \sqrt{\frac{13}{2}}\right)^{2}+\left(\sqrt{\frac{13}{2}}\right)^{2}$

$r ^{2}=\frac{65}{2}$

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