Distances to Vertices
Author: Scott Farrar
Date: 5 December 2013

Drag point D.

Find special locations for point D.

D (Drag Me)

D

D

D

C

B

A

avg

Answer #1

Compare Distances to Vertices

Clear Traces

Answer #2

A = (8.787234216084347, 1.845375553402206)
B = (14.229222198197947, 11.301312118067647)
C = (26.927194156463013, -3.3264428125780765)
poly1, c, a, b = Polygon(A, B, C)
D = (14.495883118017826, 1.768184234506976)
d = Distance(A, D)
e = Distance(B, D)
f = Distance(C, D)
E = Point(xAxis)
g = Circle(E, d)
F = Point(xAxis)
h = Circle(F, e)
G = Point(xAxis)
k = Circle(G, f)
i = OrthogonalLine(E, xAxis)
j = OrthogonalLine(F, xAxis)
l = OrthogonalLine(G, xAxis)
H = Intersect(k, l, 2)
I = Intersect(h, j, 2)
J = Intersect(g, i, 2)
m = Segment(E, J)
n = Segment(F, I)
p = Segment(G, H)
K = Intersect(xAxis, yAxis)
avgDdist: (d + e + f) / 3
q = Circle(K, avgDdist)
L = Intersect(q, yAxis, 2)
r = OrthogonalLine(L, yAxis)
M = Point(r)
t: (d - avgDdist)^(2) + (e - avgDdist)^(2) + (f - avgDdist)^(2)
a_1 = LineBisector(c)
b_1 = LineBisector(a)
N = Intersect(b_1, a_1)
c_1 = LineBisector(b)
DN = Distance(D, N)
v: DN / avgDdist
circumColorscale: 2^(v) - 1
z = false
d_1 = true
distanceDa = Distance(D, a)
TextDa: "\overline{" + (Name[D]) + (Name[a]) + "} \, = \, " + distanceDa
distanceDc = Distance(D, c)
TextDc: "\overline{" + (Name[D]) + (Name[c]) + "} \, = \, " + distanceDc
perimeterpoly1 = Perimeter(poly1)
distanceDb = Distance(D, b)
TextDb: "\overline{" + (Name[D]) + (Name[b]) + "} \, = \, " + distanceDb
distSum: Distance[B, D] + Distance[A, D] + Distance[C, D]
poly2, f_1, g_1, h_1, O = Polygon(A, B, 3)
poly3, i_1, j_1, k_1, P = Polygon(B, C, 3)
poly4, l_1, m_1, n_1, Q = Polygon(C, A, 3)
p_1 = Segment(O, C)
q_1 = Segment(P, A)
r_1 = Segment(Q, B)
R = Intersect(q_1, p_1)
s_1 = Circle(R, P)
fermatColorScale: Distance[D, R] / Distance[R, P]
t_1 = Segment(L, M)
T = Point(poly1)
U: (x(T), y(T), Distance[A, T] + Distance[B, T] + Distance[C, T])
loc1 = Locus(U, T)
S: (x(D), y(D), distSum)
s = Circle(C, Segment[B, C])
e_1 = Circle(B, a)
V = Intersect(s, e_1, 2)
c_2 = Circle(B, c)
d_2 = Circle(A, c)
W = Intersect(c_2, d_2, 2)
e_2 = Circle(C, b)
f_2 = Circle(A, b)
Z = Intersect(e_2, f_2, 1)
g_2 = Circle(A, C, Z)
h_2 = Circle(V, C, B)
k_2 = Circle(W, B, A)
a_2 = Segment(B, V)
b_2 = Segment(C, V)
i_2 = Segment(B, W)
j_2 = Segment(W, A)
l_2 = Segment(A, Z)
m_2 = Segment(Z, C)
o = false
A_1: (x(L), y(L))
B_1 = Intersect(g_2, h_2, 2)
C_1: (x(D), y(D))
n_2 = Segment(D, C)
p_2 = Segment(D, A)
q_2 = Segment(D, B)