月兒彎彎
Author: 高一忠  劉威廷

月兒彎彎

設圓P是圖中的任意一個圓，
它與圓A相切於點M(內切)，
與圓B相切於點N(外切)，又
設圓A.圓B.圓P的半徑分別是
R.r.t,那麼由此得:

 \overline{ PA }=R-t, \overline{ PB }=r+t 

→ \overline{ PA } + \overline{ PB }=R+r=定長

所以圓心P必在以A和B為
焦點，長軸等於R+r的橢
圓上。

A = Point(xAxis)
B_1 = Point(xAxis)
c = Circle(A, B_1)
B = Point(xAxis)
C = Point(c)
d = Ellipse(B, A, C)
e = Circle(B, C)
O = Intersect(xAxis, yAxis)
t = 0.6981317007977318 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
r = Segment(A, C)
M: (x(A) + r * cos(t), y(A) + r * sin(t))
s = Segment(A, M)
P = Intersect(d, s, 1.0)
w = Segment(B, P)
f = Circle(P, M)
u = Vector((0.0, y(Corner[2.0])), (0.0, y(Corner[4.0])))
v = Vector((x(Corner[1.0]), 0.0), (x(Corner[3.0]), 0.0))
T_1 = Corner(1.0)
T_4 = Corner(4.0)
D: (7.0 * Corner[4.0] + 3.0 * Corner[3.0]) / 10.0
T_2: (3.0 * Corner[2.0] + 7.0 * Corner[1.0]) / 10.0
T_3: (3.0 * Corner[3.0] + 7.0 * Corner[4.0]) / 10.0
多邊形1, t_4, t_3, t_2, t_1 = Polygon(T_4, T_3, T_2, T_1)
N = Intersect(f, w)