← etc / Encyclopedia of Triangle Centers

X₉₇₂¶

ISOGONAL CONJUGATE OF X₉₇₁

X₉₇₂ (ISOGONAL CONJUGATE OF X₉₇₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_972 = ISOGONAL CONJUGATE OF X_971."""

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


        def construct_x_00972(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_972 = ISOGONAL CONJUGATE OF X_971 on reference triangle ABC."""
            X_934 = eval_trilinear_point(model, A, B, C, '1/((b - c)*(b + c - a)**(2))', ID="X_934", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_972 = reflection_in_point(model, X_934, X_3, ID="X_972", classes=["selected", "target"], guide=False)
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_40, X_101, 40, 101, incident=True)
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            X_108 = eval_trilinear_point(model, A, B, C, 'a/(sec(B) - sec(C))', ID="X_108", classes=["center", "incident"])
            central_line(model, X_55, X_108, 55, 108, incident=True)
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", 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_109, X_165, 109, 165, incident=True)
            return promote_point_to_top(model, X_972)


        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_972 on the given reference triangle."""
            model = create_model('X_972 = ISOGONAL CONJUGATE OF X_971')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00972(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-00972.json"))
            write_center_svg(
                model_acute,
                here / "x-00972.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X972¶

X₉₇₂¶