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X₂₉₁₀¶

ORTHIC-ISOGONAL CONJUGATE OF X₄₀

X₂₉₁₀ is the orthic-isogonal conjugate of X₄₀.

X₂₉₁₀ (ORTHIC-ISOGONAL CONJUGATE OF X₄₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2910 = ORTHIC-ISOGONAL CONJUGATE OF X_40."""

        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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            mittenpunkt_of,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02910(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2910 = ORTHIC-ISOGONAL CONJUGATE OF X_40 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center"])
            X_2910 = ceva_conjugate(model, A, B, C, X_4, X_40, ID="X_2910", classes=["selected", "target"])
            X_198 = eval_trilinear_point(model, A, B, C, '(a*(cos(B) + cos(C) - cos(A) - 1))', ID="X_198", classes=["center", "incident"])
            central_line(model, X_40, X_198, 40, 198, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_1181 = eval_trilinear_point(model, A, B, C, '((1 - cos(A)*sin(B)*sin(C))*cos(A))', ID="X_1181", classes=["center", "incident"])
            central_line(model, X_9, X_1181, 9, 1181, incident=True)
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_1753 = point_from_barycentrics(model, A, B, C, -0.10341592, 0.079954955, 1.023461, ID="X_1753", classes=["center", "incident"])
            central_line(model, X_101, X_1753, 101, 1753, incident=True)
            return promote_point_to_top(model, X_2910)


        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_2910 on the given reference triangle."""
            model = create_model('X_2910 = ORTHIC-ISOGONAL CONJUGATE OF X_40')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02910(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-02910.json"))
            write_center_svg(
                model_acute,
                here / "x-02910.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2910¶

X₂₉₁₀¶