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X₂₈₉₈¶

ORTHIC-ISOGONAL CONJUGATE OF X₇

X₂₈₉₈ is the orthic-isogonal conjugate of X₇.

X₂₈₉₈ (ORTHIC-ISOGONAL CONJUGATE OF X₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2898 = ORTHIC-ISOGONAL CONJUGATE OF X_7."""

        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,
            gergonne_point_of,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02898(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2898 = ORTHIC-ISOGONAL CONJUGATE OF X_7 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center"])
            X_2898 = ceva_conjugate(model, A, B, C, X_4, X_7, ID="X_2898", classes=["selected", "target"])
            X_354 = eval_trilinear_point(model, A, B, C, '(b - c)**(2) - a*b - a*c', ID="X_354", classes=["center", "incident"])
            central_line(model, X_7, X_354, 7, 354, incident=True)
            X_857 = eval_trilinear_point(model, A, B, C, '((sin(C))**(2)*sin(2*B)*sin(C - A) + (sin(B))**(2)*sin(2*C)*sin(B - A))', ID="X_857", classes=["center", "incident"])
            X_948 = point_from_barycentrics(model, A, B, C, 0.23303835, 0.29498525, 0.4719764, ID="X_948", classes=["center", "incident"])
            central_line(model, X_857, X_948, 857, 948, incident=True)
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            X_1996 = point_from_barycentrics(model, A, B, C, 0.23108952, 0.29424011, 0.47467037, ID="X_1996", classes=["center", "incident"])
            central_line(model, X_55, X_1996, 55, 1996, incident=True)
            return promote_point_to_top(model, X_2898)


        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_2898 on the given reference triangle."""
            model = create_model('X_2898 = ORTHIC-ISOGONAL CONJUGATE OF X_7')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02898(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-02898.json"))
            write_center_svg(
                model_acute,
                here / "x-02898.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2898¶

X₂₈₉₈¶