2D 座標架
Author: 藍邦偉  老師

$ O $

$Step=%v$

$r=%v$

$Q$

$ 切點弦所在直線方程式 $

$P$

$A$

$B$

$座標平面上，\;已知\;P\;(x_0,y_0)為圓$
$C\;:x^2+y^2+dx+ey+f=0外$
$一點\;過P\;對C\;作兩切線，\;切點為$
$A,B，\;則\;\overleftrightarrow{AB}：\;x_0\;x+y_0\;y$
$+d\cdot\frac{x+x_0}{2}+e\cdot\frac{y+y_0}{2}+f=0$

$ Pf: $

$ 通過A(x_1,y_1)\;的切線L_1為 $
$x_1x+y_1y+d\cdot\frac{x+x_1}{2}$
$+e\cdot\frac{y+y_1}{2}+f=0$

$ 通過B(x_2,y_2)\;的切線L_2為 $
$x_2x+y_2y+d\cdot\frac{x+x_2}{2}$
$+e\cdot\frac{y+y_2}{2}+f=0$

$ 又\overleftrightarrow{AB}為通過A(x_1,y_1)與B(x_2,y_2)$
$的直線 $

$故\;\overleftrightarrow{AB}：\;x_0\;x+y_0\;y$
$+d\cdot\frac{x+x_0}{2}+e\cdot\frac{y+y_0}{2}+f=0$

O = (0, 0)
Q_2: 0.67 * Corner[1] + 0.33 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
s = 0 (slider from 0 to 4, step 1)
r = 2 (slider from 1 to 5, step 1)
Q_0 = (2.0484644337349347, 1.6807194400014325)
Q = DynamicCoordinates(Q_0, floor(x(Q_0)), floor(y(Q_0)))
c = Circle(Q, r)
P_0 = (7, 5)
P = DynamicCoordinates(P_0, floor(x(P_0)), floor(y(P_0)))
L_1, L_2 = Tangent(P, c)
A = Intersect(c, L_1)
B = Intersect(c, L_2)
t = 0 (slider from 0 to 2, step 0.01)
P_1: P + t * Vector[P, A]
P_2: P - t * Vector[P, A]
P_3: P + t * Vector[P, B]
P_4: P - t * Vector[P, B]
u_1 = Vector(P, P_1)
u_2 = Vector(P, P_2)
u_3 = Vector(P, P_3)
u_4 = Vector(P, P_4)
L = Polar(P, c)
a: x(P)
b: y(P)
p = 0 (slider from 0 to 2 * r, step 0.01)
A_1: A + p * Vector[A, B]
B_1: B + p * Vector[B, A]
v_1 = Vector(A, A_1)
v_2 = Vector(B, B_1)
q = 0 (slider from 0 to 1, step 0.01)
Q_a: Q + q * Vector[Q, A]
Q_b: Q + q * Vector[Q, B]
w_1 = Vector(Q, Q_a)
w_2 = Vector(Q, Q_b)
f_1 = Segment(A, Q)
f_2 = Segment(Q, B)
α = Angle(P, A, Q)
β = Angle(P, B, Q)
list = Coefficients(c)
f = Element(list, 3)
d = Element(list, 5)
e = Element(list, 6)
text5: "$\overleftrightarrow{AB}:\; " + (LaTeX[a]) + "x" + (LaTeX[If[b < 0, "-" * (-b), "+" * b]]) + "y" + (LaTeX[If[d < 0, "-" * (-d), "+" * d]]) + "\cdot\frac{x" + (LaTeX[If[a < 0, "-" * (-a), "+" * a]]) + "}{2}" + (LaTeX[If[e < 0, "-" * (-e), "+" * e]]) + "\cdot \frac{y" + (LaTeX[If[b < 0, "-" * (-b), "+" * b]]) + "}{2}" + (LaTeX[If[f < 0, "-" * (-f), If[f > 0, "+" * f, ""]]]) + "=0$"