圓的切線段長
Author: 藍邦偉　老師

圓的切線段長

 \overline{ PA }²=  \overline{ PQ } ²- \overline{ QA } ²

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
d = 5 (slider from -5 to 5, step 0.1)
e = -2 (slider from -5 to 5, step 1)
f = -4 (slider from -5 to 5, step 1)
C_1: x^(2) + y^(2) + d * x + e * y + f = 0
T_1 = Corner(1)
T_4 = Corner(4)
T_2: (3 * Corner[1] + 2 * Corner[2]) / 5
T_3: (3 * Corner[4] + 2 * Corner[3]) / 5
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
Q: ((-d) / 2, (-e) / 2)
a = Segment(T_2, T_3)
P = (3.716503362831854, 8.726580659694289)
b = Segment(Q, P)
c, g = Tangent(P, C_1)
A = Intersect(C_1, c)
B = Intersect(C_1, g)
h_1 = Segment(A, Q)
i = Segment(Q, B)
j = Segment(B, P)
k_1 = Segment(A, P)
文字4: "=[(" + (x(Q)) + (If[x(P) < 0, "+", "-"]) + (abs(x(P))) + ")²+(" + (y(Q)) + (If[y(P) < 0, "+", "-"]) + (abs(y(P))) + ")²]-" + (h_1^(2))
x_0: x(P)
y_0: y(P)
文字5: " \overline{ PA } = \sqrt{ " + (x_0^(2) + y_0^(2) + d * x_0 + e * y_0 + f) + " }"
文字8: "x²+y²" + (LaTeX[If[d < 0, "-", "+"]]) + "" + (LaTeX[abs(d)]) + "x" + (LaTeX[If[e < 0, "-", "+"]]) + "" + (LaTeX[abs(e)]) + "y" + (LaTeX[If[f < 0, "-", "+"]]) + "" + (LaTeX[abs(f)]) + "=0"