← etc / Encyclopedia of Triangle Centers

X₂₃₄₃¶

X₂-ISOCONJUGATE OF X₁₄₆₇

X₂₃₄₃ = crosssum of X₁₄₆₇ and X₂₂₅₇

X₂₃₄₃ (X₂-ISOCONJUGATE OF X₁₄₆₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2343 = X_2-ISOCONJUGATE OF X_1467."""

        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,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02343(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2343 = X_2-ISOCONJUGATE OF X_1467 on reference triangle ABC."""
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center"])
            X_220 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)**(2)', ID="X_220", classes=["center"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center"])
            X_219 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A/2)', ID="X_219", classes=["center"])
            central_line(model, X_19, X_220, 19, 220)
            central_line(model, X_57, X_219, 57, 219)
            X_2343 = intersect_lines(model, X_19, X_220, X_57, X_219, ID="X_2343", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_939 = eval_trilinear_point(model, A, B, C, '(a/(a**(4) - 2*a**(3)*(b + c) - 4*a**(2)*b*c + (b - c)*(b**(2) - c**(2))*(2*a - b - c)))', ID="X_939", classes=["center", "incident"])
            central_line(model, X_6, X_939, 6, 939, incident=True)
            return promote_point_to_top(model, X_2343)


        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_2343 on the given reference triangle."""
            model = create_model('X_2343 = X_2-ISOCONJUGATE OF X_1467')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02343(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-02343.json"))
            write_center_svg(
                model_acute,
                here / "x-02343.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2343¶

X₂₃₄₃¶