← etc / Encyclopedia of Triangle Centers

X₂₉₄₂¶

EXCENTRAL-ISOGONAL CONJUGATE OF X₇

X₂₉₄₂ is the excentral-isogonal conjugate of X₇.

X₂₉₄₂ (EXCENTRAL-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_2942 = EXCENTRAL-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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02942(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2942 = EXCENTRAL-ISOGONAL CONJUGATE OF X_7 on reference triangle ABC."""
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center"])
            X_169 = eval_trilinear_point(model, A, B, C, '- (sin(A))*(cos(A/2))**(2) + (sin(B))*(cos(B/2))**(2) + (sin(C))*(cos(C/2))**(2)', ID="X_169", classes=["center"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center"])
            X_1742 = eval_trilinear_point(model, A, B, C, '(sec(B/2))**(2) + (sec(C/2))**(2) - (sec(A/2))**(2)', ID="X_1742", classes=["center"])
            central_line(model, X_165, X_169, 165, 169)
            central_line(model, X_57, X_1742, 57, 1742)
            X_2942 = intersect_lines(model, X_165, X_169, X_57, X_1742, ID="X_2942", classes=["selected", "target"])
            X_1762 = point_from_barycentrics(model, A, B, C, 0.33791285, 0.30169303, 0.36039412, ID="X_1762", classes=["center", "incident"])
            X_2938 = point_from_barycentrics(model, A, B, C, 0.53750967, 0.44083527, 0.021655066, ID="X_2938", classes=["center", "incident"])
            central_line(model, X_1762, X_2938, 1762, 2938, incident=True)
            return promote_point_to_top(model, X_2942)


        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_2942 on the given reference triangle."""
            model = create_model('X_2942 = EXCENTRAL-ISOGONAL CONJUGATE OF X_7')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02942(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-02942.json"))
            write_center_svg(
                model_acute,
                here / "x-02942.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2942¶

X₂₉₄₂¶