← etc / Encyclopedia of Triangle Centers

X₃₀₂₈¶

INCIRCLE-ANTIPODE OF X₃₀₂₄

X₃₀₂₈ is the incircle-antipode of X₃₀₂₄.

X₃₀₂₈ (INCIRCLE-ANTIPODE OF X₃₀₂₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3028 = INCIRCLE-ANTIPODE OF X_3024."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            feuerbach_point_of,
            incenter_of,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03028(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3028 = INCIRCLE-ANTIPODE OF X_3024 on reference triangle ABC."""
            X_3024 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)*(b - c)**(2)*(b**(2) + c**(2) - a**(2) + b*c)**(2)', ID="X_3024", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_3028 = reflection_in_point(model, X_3024, X_1, ID="X_3028", classes=["selected", "target"], guide=False)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_113 = eval_trilinear_point(model, A, B, C, 'sin(B)*sin(C)*((sin(C))/(cos(C) - 2*cos(A)*cos(B)) + (sin(B))/(cos(B) - 2*cos(A)*cos(C)))', ID="X_113", classes=["center", "incident"])
            central_line(model, X_11, X_113, 11, 113, incident=True)
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center", "incident"])
            central_line(model, X_12, X_125, 12, 125, incident=True)
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_56, X_110, 56, 110, incident=True)
            return promote_point_to_top(model, X_3028)


        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_3028 on the given reference triangle."""
            model = create_model('X_3028 = INCIRCLE-ANTIPODE OF X_3024')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03028(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-03028.json"))
            write_center_svg(
                model_acute,
                here / "x-03028.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3028¶

X₃₀₂₈¶