The Python code and math for finding the coordinates of a point on the edge of a circle where a line between two points intersects on the circle, the two points being: the center of the circle (A) and the point outside of the circle (B). This math can be used to draw a line cleanly from the edge of a circle without it overlapping the circle itself.

CircleEdgePoint.py

from math import sqrt

# https://math.stackexchange.com/questions/127613/closest-point-on-circle-edge-from-point-outside-inside-the-circle

def circle_edge_point(x1, y1, x2, y2, r):
	try:
		cx = x1 + (r * (x2 - x1) / sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2))
	except ZeroDivisionError:
		# Add 0.0001 if divisor is 0
		cx = x1 + (r * (x2 - x1) / sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2) + 0.0001)

	try:
		cy = y1 + (r * (y2 - y1) / sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2))
	except ZeroDivisionError:
		cy = y1 + (r * (y2 - y1) / sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2) + 0.0001)

	# Return x,y of C-coord as a list
	return [cx, cy]


c_coords = circle_edge_point(0, 0, 3.6, 4, 3)

print(c_coords)

graph.png

math.png

use case.png