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X₂₉₉₉¶

DANNEELS-BEVAN HOMOTHETIC CENTER

Let \(R_{A}\) be the radical axis of the Bevan circle and the A-excircle. Define \(R_{B}\) and \(R_{C}\) cyclically. The three radical axes form a triangle homothetic to triangle ABC, and X₂₉₉₉ is the center of homothety. (Eric Danneels, Hyacinthos #10926, Dec. 5, 2004.

X₂₉₉₉ (DANNEELS-BEVAN HOMOTHETIC CENTER) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2999 = DANNEELS-BEVAN HOMOTHETIC CENTER."""

        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,
            incenter_of,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02999(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2999 = DANNEELS-BEVAN HOMOTHETIC CENTER on reference triangle ABC."""
            X_2297 = point_from_barycentrics(model, A, B, C, 0.32383634, 0.32946828, 0.34669538, ID="X_2297", classes=["center"])
            X_2999 = isogonal_conjugate(model, A, B, C, X_2297, ID="X_2999", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_1, X_2, 1, 2, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            central_line(model, X_6, X_57, 6, 57, incident=True)
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center", "incident"])
            central_line(model, X_31, X_165, 31, 165, incident=True)
            return promote_point_to_top(model, X_2999)


        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_2999 on the given reference triangle."""
            model = create_model('X_2999 = DANNEELS-BEVAN HOMOTHETIC CENTER')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02999(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-02999.json"))
            write_center_svg(
                model_acute,
                here / "x-02999.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2999¶

X₂₉₉₉¶