Hi PEER,

The center of the tangent circle must be equidistant from the line endpoint, and the red arc, and Also be on a horizontal line through the line endpoint.
Not sure how to do such constraints.

- Brian

Copy the Red circle to make it tangent to the line endpoint, on the left side.
Draw a line between the two red circle centers, and find the midpoint, and perpendicular bisector line. This line intersects the horizontal line thru the line endpoint.
This is the center of the desired tangent circle. Then draw said circle.

(isosceles triangle.)