Circle with center point and tangential to lines

Question

I have defined Points all points (3 blue, and one green). All points have the same distance to A point. Yellow lines are bisectors. I have equations of AB and AC with Ax + By +C = 0 form.

I need construct circle (tangential to lines) with green point center. Any hint or steps? BR

Answer 1

You should find two things:

1. Center of the circle: it's green points: $G=(x_1,y_1)$.
2. Radius of the circle: it's a distance from a point $G$ to a line $Ax+By+C=0$ (see here):

$$r=\frac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}$$

Equation of the circle is:

$$(x-x_0)^2+(y-y_0)^2=r^2$$

Answer 2

Construct a line through the green point perpendicular to one of the two lines. You now have the radius of your circle (distance from the green point to the intersection of that perpendicular line and the other line). Now draw the circle with that radius and you're done.

EDIT: I assumed the OP meant construction using a ruler and a compass. This can also be done analytically in a very similar way. The main difference being that the perpendicular line must be found analytically (I recommend using vectors).