Title: Find the tangent lines between a point and a circle in Python

[A circle and its tangent lines starting at a point]

Finding the tangent lines between a point and a circle isn't too hard if you're familiar with the example Determine where two circles intersect in Python.
[A circle and its tangent lines starting at a point] Consider the figure on the right. R is the radius of the circle. You can easily calculate the distance D between the external point and the circle's center by using the Pythagorean theorem. If the point P is (Px, Py) and the circle's center C is (Cx, Cy), then .

The tangent meets the circle's radius at a 90 degree angle so you can use the Pythagorean theorem again to find .

Believe it or not, you're now done because the tangent points P0 and P1 are the the points of intersection between the original circle and the circle with center P and radius L. Simply use the code from the example Determine where two circles intersect in Python to find those points.

The following code shows how the find_point_circle_tangents method used by the example program finds the tangent points.

def find_point_circle_tangents(center, radius, point): ''' Return the tangent points for the segments between a circle and an external point. ''' # Find the distance squared from the # external point to the circle's center. dx = center[0] - point[0] dy = center[1] - point[1] dist_squared = dx * dx + dy * dy if dist_squared < radius * radius: # The point is inside the circle. Return None. return None # Find the distance from the external point # to the tangent points. tangent_dist = math.sqrt(dist_squared - radius * radius) # Find the points of intersection between # the original circle and the circle with # center at the point and radius tangent_dist. intersections = find_circle_circle_intersections( center, radius, point, tangent_dist) return intersections

The code calculates the distance D squared. It uses that to calculate L and then calls find_circle_circle_intersections to find the intersections between the two circles. See the previous example for a description of the find_circle_circle_intersections method.

Download the example to see all of the details.