**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:

$3 \sqrt{5}$

$5 \sqrt{3}$

$5 \sqrt{4}$

$4 \sqrt{5}$

Correct Option: 1

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

$h=8$

center $(8,2)$