The line

Question:

The line $2 x-y+1=0$ is a tangent to the circle at the point $(2,5)$ and the centre of the circle lies on $x-2 y=4$. Then, the radius of the circle is:

  1. $3 \sqrt{5}$

  2. $5 \sqrt{3}$

  3. $5 \sqrt{4}$

  4. $4 \sqrt{5}$


Correct Option: 1

Solution:

$\left(\frac{h-\frac{(h-4)}{2}}{2-h}\right)(2)=-1$

$h=8$

center $(8,2)$

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