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

Options

A. `3 sqrt(5)`
B. `5 sqrt(3)`
C. `2sqrt(5)`
D. `5 sqrt(20`

Answer

A

Explanation

`2x-y+1=0` is a tangent.
Slope of line `OA = -(1)/(2)`

The equation of OA is
`(y-5)=-(1)/(2)(x-2)`
or `x+2y=12`
Therefore , intersection with `x-2y=4` will give the coordinates of centre as `(8,2)` . Hence,
`r=OA=sqrt((8-2)^(2)+(2-5)^(2))=3sqrt(5)`