Question 1086213
.
There is the third way to solve this problem.


It is to find the center as the intersection of two straight lines.


One line is the perpendicular to the given line at the tangent point,
and the other line is the perpendicular bisector to the segment, connecting two given points.


In this way you need to solve only one system of two linear equations,
and you avoid solving the quadratic equation.



For many solved problems/samples of this kind see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Find-the-equation-of-the-circle-given-by-its-center-and-tauching-a-given-line.lesson>Find the standard equation of a circle</A>

in this site.