A = (-3, 4)
B = (-4, -2)
C = (4, -2)
ABC, c_1, a_1, b_1 = Polygon(A, B, C)
P = PointIn(ABC)
PAB, b_2, p_2, a_3 = Polygon(P, A, B)
PAC, c_3, p_3, a_4 = Polygon(P, A, C)
a = Segment(B, C)
U = Point(a)
PBU, u, p, a_2 = Polygon(P, B, U)
kv4: ((2 * ABC / 3)) / PBU
PCU, u_1, p_1, c_2 = Polygon(P, C, U)
cv2: PCU + PAC ≥ ABC / 3
kv1: ABC / ((3 * PCU))
cv1: PCU ≥ ABC / 3
kv2: (ABC / 3 - PCU) / PAC
cv3: PCU + PAC + PAB ≥ ABC / 3
kv3: (ABC / 3 - PCU - PAC) / PAB
c = Segment(A, B)
b = Segment(C, A)
V = If(cv1, Dilate[C, kv1, U], If[cv2, Dilate[A, kv2, C], If[cv3, Dilate[B, kv3, A], Dilate[B, kv4, U]]])
f = Segment(P, U)
P1 = If(cv1, Polygon[P, U, V], If[cv2, Polygon[P, U, C, V], If[cv3, Polygon[P, U, C, A, V], Polygon[P, U, C, A, B, V]]])
g = Segment(P, V)
cv4: PBU ≥ (2 * ABC / 3)
cw1: PBU ≥ ABC / 3
cw2: PBU + PAB ≥ ABC / 3
cw3: PBU + PAB + PAC ≥ ABC / 3
kw1: ABC / ((3 * PBU))
kw2: (ABC / 3 - PBU) / PAB
kw3: (ABC / 3 - PBU - PAB) / PAC
kw4: (2 * ABC / ((3 * PCU)))
W = If(cw1, Dilate[B, kw1, U], If[cw2, Dilate[A, kw2, B], If[cw3, Dilate[C, kw3, A], Dilate[C, kw4, U]]])
P2 = If(cw1, Polygon[P, U, W], If[cw2, Polygon[P, U, B, W], If[cw3, Polygon[P, U, B, A, W], Polygon[P, U, B, A, C, W]]])
h = Segment(P, W)
PU: U
PP: P