How to find radius?

Question

When I am given centre of circle and a tangent of the circle. How can I get radius? I know radius is perpendicular to tangent so I applied distance foormula but what I got is ^2 of actual answer

Answer 1

If you have the line $ax+by + c = 0$

and a point not on the line $(x_1,y_1)$

The distance of a point from the line: $\frac {|ax_1 + by_1 + c|}{\sqrt {a^2 + b^2}}$

Answer 2

Distance between point $(x_0, y_0)$ and line $ax + by+ c=0$ is
$\qquad\frac {|ax_0 + by_0 + c|}{\sqrt {a^2 + b^2}}= radius$
Your most probable mistake might be that you took $radius = r^2$ from equation of circle $x^2 + y^2 = r^2$

Answer 3

find the length of perpendicular from centre of the circle to the tangent.

if the equation of tangent is $ax+by+c$, the radius is, $$ r = \left|\frac{ax_c+by_c+c}{\sqrt{a^2+b^2}}\right|$$

where, $x_c$ and $y_c$ are coordinates of center.