I am facing a problem that I have difficulty to solve.
I have a line that originates from the origin (point $(0,0)$) and has a known angle to the $x$ axis (angle $\theta$)
Somewhere between the $x$ axis and this line is a circle. This circle touches both lines, but the dimension and center of this circle are not known.
On the right side of the circle is a point $P$ that lies on the circumference of the circle and of which the coordinates are known.
How can I find the coordinates of the center of the circle?
I can't seem to add an image so I have used an external website to make the drawing.
I now realize that I have over-simplified the problem because it is hard to explain in words. However, now I know that I can send a drawing in another way I would like to post the original problem:
You can see the drawing over here
There are two lines originating from the origin. The angle of each line in relation to the diagonal is the same and is known. A circle is centered on the diagonal and only a 90 degrees arc of the circle is drawn between the lines. On the arc of the circle is a point P of which the coordinates are known. The dimension and location of the circle is not known, the only thing that is known is that point P lies on the arc and the arc is a 90 degrees segment of a circle with its center on the diagonal.
How can I find the coordinates of the circle?