Determine center of circle if radius and 2 tangent line segments are given Given the radius and its $2$ tangent lines and their point of intersection of a circle.
A similar question is 
How to calculate the two tangent points to a circle with radius R from two lines given by three points
But how do I find coordinates of the center of the circle.
I believe there must be $2$ solutions—each side of the intersection point.
Please let me know what I am doing wrong am here, or if I am missing something?
Thanks in advance.

 A: You have equation of two tangents.
STEP $1$:Draw perpendicular(normal) from centre to tangents it is equal to radius.since you have two tangents you will draw two perpendicular(normal). 
STEP $2$ :so you will get two equation consists of coordinates of centre.
STEP $3$: Then solve those equation you will get coordinates of centre.If you dont know how to draw perpendicular let me know and give data I'll solve it.
A: The question is tagged (geometry) not (analytic-geometry), so I assume you need to solve the problem by a construction, not calculation. Here are first four steps:


*

*Let your given lines be denoted as $a$ and $b$.

*Construct lines $f$ and $g$ on both sides of the given line $a$, parallel to $a$, at a distance $R$ from $a$.

*Similary construct lines $k$ and $l$, parallel to $b$, $R$ apart from it.

*Find four intersection points, say $P_1$ through $P_4$, of $f$ and $g$ with $k$ and $l$. These are center points of four circles with radius $R$, tangent to the two given lines.


Here additional question comes: are you given two lines, as the question states, or two line segments, as in the title? If there are two tangent lines, you're done at step 4. However if you have two line segments, you need to check, if the tangency points are in the segments. Then:


*For each $P_i$ draw two lines, one perpendicular to $a$ and the other one to $b$. Check if they meet $a$ and $b$, respectively, inside the given segments. If so, the $P_i$ is a center point of the circle sought. Otherwise discard it.


Note that the solution may contain from zero up to four circles, depending on the line segments configuration.
A: There is also another possibility to solve this problem. 


*

*If you know the three points A, B, C (B is the crossing point) you can determine the directional vectors of the lines: v1 = A - B and v2 = C - B. It is better to make them unit vectors by dividing by the lengths.

*From the two directional vectors you can find the angle alpha between them from the dot product definition.

*Then you can find the distance from the middle point B to the centre of the circle O as |BO| = R / sin(alpha).

*and the coordinates of the centre O as: O = B + BO, where BO is a unit vector. In the same time you have enough data to find the distance from B to your tangent points and their coordinates.
This approach will work for both 2- and 3-dimensional rectangular CS.
