1
$\begingroup$

Probably simple to solve but I'm a bit stuck. I am given two lines that are tangent to a circle and the circle must go through $P_1$ (which is the end of Line 1) and $P_2$ (which is the end of Line 2).

How do I calculate the Center Point of that circle? With given lines and points it should be only one solution.

  • 2
    Calculate the lines orthogonal to your given lines through the given points. Their intersection is the center.2012-09-05
  • 0
    This is of course over-determined (which implies that there is not always a solution). Construct the angular bisctor(s) of the two lines $l_1$ and $l_2$ (or the middle parallel if they ar parallel) and intersect it with the line orthogonal to $l_1$ through $P_1$ to find the center (or two candidates). We do not need the point $P_2$ at all, only a hint, on which side the circle should touch $l_1$.2012-09-05
  • 0
    One thing i know is that the lines will never be parallel and that the circle is on the side of the lines where the angle from l1 to l2 is smaller.2012-09-05

1 Answers 1