Right Triangle Altitude Theorem
Author: Irena Štrasuová

Right Triangle Altitude Theorem - legs

See also "Right Triangle Altitude Theorem - Altitude"

C'

v

c

a

c

c_a

leg a

c

c_b

leg b

b²

c·c_b

=

$ a^2 $

=

$ c·c_a $

Euclid’s theorem of leg

CHOOSE LEG AND THEN
MOVE THE RED POINT

s = 0 (slider from 0 to 4, step 0.1)
gamma = If(s < 2.6, 0, If[s < 3.6, s - 2.6, 1])
B = (7.74, 0.46)
A = (2.64, 0.42)
q = Circle(A, B)
a = Segment(A, B)
r = OrthogonalLine(A, a)
N, P = Intersect(q, r)
O = Midpoint(a)
c = Circle(O, B)
C = Point(c)
e = OrthogonalLine(C, a)
F = Intersect(a, e)
f = Segment(C, F)
d_1 = Circle(C, gamma * f)
R, V = Intersect(d_1, f)
mnohoúhelník1, d, a_1, b = Polygon(A, B, C)
p_1 = Circle(R, d)
C_1, D_1 = Intersect(p_1, e)
j_2 = Line(C, B)
mnohoúhelník4, a_2, c_2, n, p, L, M = Polygon(A, C, 4)
alfa = If(s < 0.3, 0, If[s < 1.3, s - 0.3, 1])
t = Circle(C, a_1 * alfa)
α = Angle(A, C, B)
D = Intersect(a, d)
E = Intersect(a, d)
mnohoúhelník2, c_1, b_1, g, h, G, H = Polygon(C, B, 4)
k = Circle(B, A)
i = OrthogonalLine(B, a)
I, J = Intersect(k, i)
j = OrthogonalLine(F, a)
l = OrthogonalLine(I, j)
K = Intersect(l, j)
mnohoúhelník3, f_1, k_1, i_1, b_2 = Polygon(F, K, I, B)
m = false
mnohoúhelník5, a_3, n_1, k_2, f_2 = Polygon(A, N, K, F)
o = false
beta = If(s < 1.5, 0, If[s < 2.5, s - 1.5, 1])
mnohoúhelník8, j_1, l_1, m_1, r_1 = Polygon(A, R, C_1, N)
A' = Rotate(A, -((beta * 90)°), A)
e_1 = Circle(C, alfa * b)
B' = Rotate(B, (beta * 90)°, B)
h_1 = Circle(C, gamma * f)
A'_1 = Rotate(A, -((beta * 90)°), A)
Q, S_1 = Intersect(t, a_1)
q_1 = Circle(Q, b)
Z, A_1 = Intersect(q_1, j_2)
mnohoúhelník6, m_2, a_4, q_2, z = Polygon(M, A, Q, Z)
M' = Rotate(M, -((beta * 90)°), A)
A'_2 = Rotate(A, -((beta * 90)°), A)
Q' = Rotate(Q, -((beta * 90)°), A)
Z' = Rotate(Z, -((beta * 90)°), A)
mnohoúhelník6', m', a'_2, q', z' = Polygon(M', A'_2, Q', Z')
S, T_1 = Intersect(e_1, b)
g_1 = Circle(S, a_1)
s_1 = Line(C, A)
T, U = Intersect(g_1, s_1)
mnohoúhelník7, b_3, s_2, t_1, g_2 = Polygon(B, S, T, G)
B'_1 = Rotate(B, (beta * 90)°, B)
S' = Rotate(S, (beta * 90)°, B)
T' = Rotate(T, (beta * 90)°, B)
G' = Rotate(G, (beta * 90)°, B)
mnohoúhelník7', b'_1, s', t', g' = Polygon(B'_1, S', T', G')
W, B_2 = Intersect(h_1, f)
d_2 = Circle(W, d)
B_1 = Intersect(d_2, f_1)
mnohoúhelník9, b_4, w, b_5, i_2 = Polygon(B, W, B_1, I)