X7¶
GERGONNE POINT
Let Ta, Tb, Tc denote the points in which the incircle meets the sides BC, CA, AB, respectively. The lines ATa, BTb, CTc concur in X7.
X7 (GERGONNE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶
"""GEOMETOR construction model for X_7 = GERGONNE POINT."""
from __future__ import annotations
from pathlib import Path
import sympy.geometry as spg
from geometor.model import Model
from geometor.etc.ops import (
central_line,
centroid_of,
construct_baseline_triangle,
create_model,
eval_trilinear_point,
gergonne_point_of,
incenter_of,
mittenpunkt_of,
nagel_point_of,
promote_point_to_top,
)
from geometor.etc.render import write_center_svg
def construct_x_00007(
model: Model, A: spg.Point, B: spg.Point, C: spg.Point
) -> spg.Point:
"""Construct X_7 = GERGONNE POINT on reference triangle ABC."""
X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["selected", "target"], draw_cevians=True)
X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
central_line(model, X_2, X_9, 2, 9, incident=True)
X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
central_line(model, X_1, X_20, 1, 20, incident=True)
X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
central_line(model, X_8, X_65, 8, 65, incident=True)
return promote_point_to_top(model, X_7)
def build_model(
sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
show_guides: bool = False,
) -> Model:
"""Build a `geometor.model.Model` for X_7 on the given reference triangle."""
model = create_model('X_7 = GERGONNE POINT')
A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
construct_x_00007(model, A, B, C)
return model
if __name__ == "__main__":
here = Path(__file__).resolve().parent
model_acute = build_model((5.0, 6.0, 7.0))
model_acute.save(str(here / "x-00007.json"))
write_center_svg(
model_acute,
here / "x-00007.svg",
subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
)