← etc / Encyclopedia of Triangle Centers

X₂₉₄₃¶

EXCENTRAL-ISOGONAL CONJUGATE OF X₈

X₂₉₄₃ is the excentral-isogonal conjugate of X₈.

X₂₉₄₃ (EXCENTRAL-ISOGONAL CONJUGATE OF X₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2943 = EXCENTRAL-ISOGONAL CONJUGATE OF X_8."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02943(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2943 = EXCENTRAL-ISOGONAL CONJUGATE OF X_8 on reference triangle ABC."""
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center"])
            X_978 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c) + a*(b**(2) - b*c + c**(2)) - b*c*(b + c)', ID="X_978", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_1106 = eval_trilinear_point(model, A, B, C, '((1 - cos(A))**(2))', ID="X_1106", classes=["center"])
            central_line(model, X_40, X_978, 40, 978)
            central_line(model, X_1, X_1106, 1, 1106)
            X_2943 = intersect_lines(model, X_40, X_978, X_1, X_1106, ID="X_2943", classes=["selected", "target"])
            X_517 = eval_trilinear_point(model, A, B, C, '-1 + cos(B) + cos(C)', ID="X_517", classes=["center", "incident"])
            X_1046 = point_from_barycentrics(model, A, B, C, 0.13236391, 0.3064877, 0.5611484, ID="X_1046", classes=["center", "incident"])
            central_line(model, X_517, X_1046, 517, 1046, incident=True)
            return promote_point_to_top(model, X_2943)


        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_2943 on the given reference triangle."""
            model = create_model('X_2943 = EXCENTRAL-ISOGONAL CONJUGATE OF X_8')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02943(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-02943.json"))
            write_center_svg(
                model_acute,
                here / "x-02943.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2943¶

X₂₉₄₃¶