數與數線(7)
Author: 藍邦偉　老師

A

B

C

D

∵\Delta ABD≈\Delta DBC∴\overline{BD}²=\overline{AB}×\overline{BC}

⇒\overline{BD}²=(3+2\sqrt{3})(-9+14\sqrt{3})

=-27+42\sqrt{3}-18\sqrt{3}+84=57+24\sqrt{3}

⇒\overline{BD}=\sqrt{57+24\sqrt{3}}=\sqrt{57+2\sqrt{12²×3}}=\sqrt{48}+\sqrt{9}=3+4\sqrt{3}

A = (4.72, -0.9)
B: A + (5, 0)
a = Segment(A, B)
c = Semicircle(A, B)
C = Point(a)
b = OrthogonalLine(C, a)
D = Intersect(c, b)
d = Segment(D, C)
n = 0 (slider from 0 to 5, step 1)
e = Segment(D, A)
f = Segment(D, B)
E = (-1.74, 1.44)
E_1: E + (1.2, 0)
E_3: E + (0, 0.6)
E_2: E_1 + E_3 - E
poly1, e_1, e_2, e_3, e_4 = Polygon(E, E_1, E_2, E_3)