如何从数学上从一个点找到圆中的外点？

Question

尝试找到一组点，使一个点看似连接到一个圆，如下图所示，但没有重叠，并且与圆的边缘对齐。抱歉，如果这很难理解，很难解释。

Answer 1

如果你想要这样的东西：

然后下面的Python代码就可以做到这一点。

import numpy as np

# function that calcuates the points at which the lines are tangent to the circle
def tangent_points(Point, Circle):
    Rot_90 = np.array([[0, -1], 
                       [1, 0]]) 
    O = Circle[0]
    r = Circle[1]
    unit_OP = Point - O
    OP = np.sqrt( unit_OP.dot(unit_OP) )
    unit_OP = unit_OP / OP
    a = r**2 / OP
    unit_perp = Rot_90.dot(unit_OP)
    b = np.sqrt(r**2 - a**2)
    return O + a*unit_OP + b*unit_perp, O + a*unit_OP - b*unit_perp

# Test example 
O = np.array([0,0])
r = 2
P = np.array([7,5])   
Circ = (O, r)
  
T1, T2 = tangent_points(P, Circ)

# plotting preparations:

# prepare circle
s = np.linspace( 0 , 2 * np.pi , 150 )
xc = O[0] + r*np.cos( s )
yc = O[1] + r*np.sin( s )

# prepare tangents
s = np.linspace( 0, 1, 150)  
L1 = P[:, np.newaxis]*(1-s[np.newaxis, :]) + T1[:, np.newaxis]*s[np.newaxis, :]
L2 = P[:, np.newaxis]*(1-s[np.newaxis, :]) + T2[:, np.newaxis]*s[np.newaxis, :]

# actual plotting
# setup a figure environment
figure, axes = plt.subplots()
axes.set_aspect( 1 )
# plotting circle and center
axes.plot( xc, yc )
axes.plot(O[0], O[1], 'bo')
# plotting point ouside circle
axes.plot(P[0], P[1], 'bo')

# plotting tagnetn lines
axes.plot( L1[0], L1[1] )
axes.plot( L2[0], L2[1] )

# plotting tangent points
axes.plot(T1[0], T1[1], 'ro')
axes.plot(T2[0], T2[1], 'ro')

plt.show()   

Answer 2

@Futurlogger，我们如何用 Javascript 编写这个？