I am trying to figure out how to calculate a tangent point on arc given a point on the arc (the midpoint) and the arc's radius.
I have a diagram:
The two red lines that come to a point are the current lines. They meet at a point, let's say (0,-0.1). I need to basically move these lines to the blue position which is parallel to the original lines or tangent to another point (relatively far away, about (4.769,-5.238)). Finally, the two lines need to be connected with an arc that has a radius of 0.1.
All I need are the points on that arc/imaginary circle that are tangent to the other point or parallel to the red lines (not sure which is better/easier) and results in the 0.1 radius arc's midpoint curving up to the 0.1 distance as pictured.
I've included the answers in purple, but since I'm using a CAD program, I need to determine the formula or method for reaching those answers.
It is similar to this question: How to calculate the two tangent points to a circle with radius R from two lines given by three points
Except the point P still needs to be on the arc.