チェバの定理

3つの直線が１点で交わるようにスライダーを調整しよう。

スライダーを動かして
３つの黒い線分が1点で交わるように
四角い頂点を動かしてみよう．

そのときの辺の比の計算がどうなるかを
観察しよう．

×

×

チェバの定理

A

B

B

C

C

A

a_1 = 1 (slider from 0 to 5, step 1)
A = (4.54, 4.8)
G = (7.72, 5.06)
H = (9.28, 5.06)
n = Segment(G, H)
I = (9.76, 5.06)
J = (11.38, 5.06)
p = Segment(I, J)
K = (11.84, 5.06)
L = (13.42, 5.08)
q = Segment(K, L)
B = (-1.2662, -3.37942)
a_2 = 2 (slider from 0 to 4, step 1)
a_3 = 3 (slider from 0 to 6, step 1)
C = (11.2694, -4.08122)
a = Segment(A, B)
b = Segment(B, C)
c = Segment(C, A)
h = Circle(A, (a * a_1 / 5))
P = Intersect(h, a, 1)
i = Segment(P, C)
d = Circle(B, (b * a_2 / 4))
e = Circle(C, (c * a_3 / 6))
Q = Intersect(d, b, 1)
R = Intersect(e, c, 1)
f = Segment(A, Q)
g = Segment(B, R)
j = Segment(A, P)
k = Segment(P, B)
l = Segment(B, Q)
m = Segment(Q, C)
r = Segment(C, R)
s = Segment(R, A)
テキスト7: "" + a_1 + ""
b_1: 5 - a_1
b_2: 4 - a_2
b_3: 6 - a_3
テキスト13: "" + b_1 + ""
テキスト14: "" + a_2 + ""
テキスト15: "" + b_2 + ""
テキスト16: "" + a_3 + ""
テキスト17: "" + b_3 + ""
c_1: ((a_1 * a_2) * a_3 / b_1 / b_2 / b_3)
テキスト18: "=" + c_1 + ""