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I am trying to find the centre and radius of a circle passing through a known point, and that is also tangential to two known lines. The only knowns are:

  • Line 1 (x1,y1) (x2,y2)
  • Line 2 (x3,y3) (x4,y4)
  • Known Point (xp,yp)

From that I need to calculate the centre of the circle (x,y).

Any help would be greatly appreciated.

Regards

Martin.

  • 1
    This is a [special case of the Apollonius problem](http://en.wikipedia.org/wiki/Special_cases_of_Apollonius%27_problem#Type_3:_One_point.2C_two_lines_.28PLL.2C_generally_2_solutions.29) so there are typically two solutions (unless the point lies on one of the lines, or the lines are parallel and the point is not between them, or the lines are not distinct). Clearly the circles' centres lie on a line halfway between the original two lines (an angle bisector if they cross).2011-06-07

4 Answers 4