投影定理
Author: 藍邦偉　老師

a=bcosC+ccosB,b=acosC+ccosA,c=acosB+bcosA

投影定理

a=bcosC+ccosB

b=acosC+ccosA

c=acosB+bcosA

bcosC

ccosB

a

ccosA

acosC

b

ccosB

bcosC

c

c

b

a

A = (8.651949910554562, 4.162754919499106)
B = (4, 0)
C = (10, 0)
多邊形1, c, a, b = Polygon(A, B, C)
d = Circle(A, B, C)
n = 2 (slider from 0 to 4, step 1)
α = Angle(B, A, C)
β = Angle(C, B, A)
γ = Angle(A, C, B)
r = Radius(d)
e = LineBisector(B, C)
f = LineBisector(A, C)
g = OrthogonalLine(A, a)
D = Intersect(g, a)
h = OrthogonalLine(B, b)
E = Intersect(h, b)
i = OrthogonalLine(C, c)
F = Intersect(i, c)
h_a = Segment(A, D)
h_b = Segment(E, B)
h_c = Segment(F, C)
j = LineBisector(B, D)
k = LineBisector(D, C)
p = Circle(D, C)
q = Circle(B, D)
G, H = Intersect(p, k)
s = CircleArc(H, D, C)
I, J = Intersect(q, j)
t = CircleArc(J, B, D)
l = LineBisector(B, C)
K = Intersect(l, a)
c_1 = Circle(K, B)
L = Point(l)
d_1 = CircleArc(L, C, B)
m = LineBisector(A, E)
a_1 = LineBisector(E, C)
M = Point(m)
N = Point(a_1)
e_1 = CircleArc(M, E, A)
f_1 = CircleArc(N, C, E)
b_1 = LineBisector(A, C)
O = Point(b_1)
g_1 = CircleArc(O, A, C)
h_1 = LineBisector(B, F)
i_1 = LineBisector(F, A)
P = Point(i_1)
Q = Point(h_1)
k_1 = CircleArc(Q, F, B)
p_1 = CircleArc(P, A, F)
j_1 = LineBisector(B, A)
R = Point(j_1)
q_1 = CircleArc(R, B, A)