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I'm trying to find a 'characteristic' line of a polygon. Therefore I would like to find the center of a cirkel enclosed by 2 lines, with it's center on a perpendicular bisector.

I've made an illustration with geogebra, the green lines are perpendicular, A B C and D are known, but F is unknown.

My intuition tells me there is a pretty easy correlation to find the coordinates of F, but either my maple or just general math skills aren't enough.

Circle enclosed between 2 lines

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The center of a circle tangent to two fixed lines must lie on their angle bisector. After all, the center of such a circle is equidistant from those lines, and that’s exactly what characterizes points on their bisectors. So, you just need to find the intersection of this angle bisector with the other line on which the center of the circle must lie. The radius is easy to compute once you have that.

However, in general there will be two angle bisectors, so there will be two possible solutions. You will need to come up with some other criteria for selecting the one you’re interested in. Another consideration is that if the circle must be tangent to two line segments instead of two lines, there might not be any solution at all.

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