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X₃₀₇₈¶

DANNEELS POINT OF X₅

Let A'B'C' be the cevian triangle of a point X =\(x : y : z\) (trilinears), let L(A) be the line through A parallel to B'C', and define L(B) and L(C) cyclically. The lines L(A), L(B), L(C) form a triangle homothetic to A'B'C', with homothetic center

X₃₀₇₈ (DANNEELS POINT OF X₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3078 = DANNEELS POINT OF X_5."""

        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,
            ceva_conjugate,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03078(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3078 = DANNEELS POINT OF X_5 on reference triangle ABC."""
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center"])
            X_233 = eval_trilinear_point(model, A, B, C, '(b*cos(C - A) + c*cos(B - A))*cos(B - C)', ID="X_233", classes=["center"])
            X_3078 = ceva_conjugate(model, A, B, C, X_5, X_233, ID="X_3078", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            return promote_point_to_top(model, X_3078)


        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_3078 on the given reference triangle."""
            model = create_model('X_3078 = DANNEELS POINT OF X_5')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03078(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-03078.json"))
            write_center_svg(
                model_acute,
                here / "x-03078.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3078¶

X₃₀₇₈¶