Soru:

Çözüm:

ABC üçgeninin yüksekliğine h diyelim.
P den BC ye paralel çizerek AB ve AC kenarlarını kestiği noktalar K ve L olsun.

h

a = 5 (slider from 1 to 10, step 1)
b = 6 (slider from 1 to 10, step 1)
c = 8 (slider from 1 to 10, step 1)
A = (-1.559448095802453, 7.723678156891599)
d = Circle(A, (2 * (a + b + c) / 3^(0.5)))
B_{1} = (4.593908155552465, -3.014386371933512)
A_{1} = (-0.8649705626770763, -2.3254016793414345)
metin6: "Buna \;göre \;A(ABC) = \frac{" + (LaTeX[(a + b + c)^(2)]) + "}{\sqrt{3}} \;birim\;karedir."
e = Circle(A, ((b + c - a) * 2 / 3^(0.5)))
B = Point(e)
f = Segment(A, B)
g = Circle(B, Distance[A, B])
C = Intersect(e, g, 1)
h = Segment(B, C)
i = Segment(C, A)
j = Ray(A, B)
k = Ray(A, C)
l = OrthogonalLine(B, h)
p = Circle(B, a)
D_{1} = Intersect(p, l, 1)
m = OrthogonalLine(D_{1}, l)
q = Circle(B, b)
n = OrthogonalLine(B, f)
E_{1} = Intersect(q, n, 2)
r = OrthogonalLine(E_{1}, n)
P = Intersect(m, r)
t = OrthogonalLine(P, h)
G = Intersect(t, h)
f_1 = OrthogonalLine(P, f)
F = Intersect(f_1, j)
s = OrthogonalLine(P, k)
F_{1} = Intersect(s, i)
i_1 = Segment(P, F)
h_1 = OrthogonalLine(P, k)
E = Intersect(k, h_1)
j_1 = Segment(P, E)
k_1 = Line(B, C)
g_1 = OrthogonalLine(P, k_1)
D = Intersect(g_1, k_1)
l_1 = Segment(P, D)
ü1, c_1, b_1, p_1 = Polygon(B, P, C)
m_1 = Segment(C, D)
metin2: "ABC eşkenar üçgen. PD⟂BC, PE⟂AC, PF⟂AB
|PD|=" + a + " birim, |PE|=" + c + " birim, |PF|=" + b + " birim olduğuna göre A(BPC) kaç birim² dir?"
r_1 = OrthogonalLine(A, h)
H = Intersect(r_1, h)
s_1 = Segment(A, H)
n_1 = Line(P, h)
K = Intersect(n_1, j)
L = Intersect(n_1, k)
q_1 = Segment(K, L)
metin5: "AKL eşkenar üçgeninde |PF|+|PE|=h+|PD| ise h= |PF|+|PE|-|PD| 
h=" + i_1 + "+" + j_1 + "-" + l_1 + " = " + (i_1 + j_1 - l_1) + " birim."
metin7: "ABC \;üçgeninin \;bir \;kenarına \;a \;yüksekliğine \;h \;dersek\; 
\\h=\frac{a\sqrt{3}}{2} \;den \;a=\frac{2h}{\sqrt{3}} \; yani \;a=\frac{" + (LaTeX[(2 * (b + c - a))]) + "}{\sqrt{3}} \;olur."
metin8: "Buna \;göre \;A(PBC) =\frac{|BC|.|PD|}{2}=\frac{" + (LaTeX[(2 * (b + c - a))]) + "." + (LaTeX[a]) + "}{2.\sqrt{3}} = \frac{" + (LaTeX[((b + c - a) * a)]) + "}{\sqrt{3}}\;bulunur."