← etc / Encyclopedia of Triangle Centers

X₃₁₁¶

ISOTOMIC CONJUGATE OF X₅₄

X₃₁₁ (ISOTOMIC CONJUGATE OF X₅₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_311 = ISOTOMIC CONJUGATE OF X_54."""

        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,
            isotomic_conjugate,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00311(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_311 = ISOTOMIC CONJUGATE OF X_54 on reference triangle ABC."""
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center"])
            X_311 = isotomic_conjugate(model, A, B, C, X_54, ID="X_311", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_4, X_69, 4, 69, incident=True)
            X_22 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4))', ID="X_22", classes=["center", "incident"])
            X_157 = eval_trilinear_point(model, A, B, C, '(a*(b**(3)*cos(B) + c**(3)*cos(C) - a**(3)*cos(A)))', ID="X_157", classes=["center", "incident"])
            central_line(model, X_22, X_157, 22, 157, incident=True)
            X_95 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*sec(B - C)', ID="X_95", classes=["center", "incident"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            central_line(model, X_95, X_99, 95, 99, incident=True)
            return promote_point_to_top(model, X_311)


        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_311 on the given reference triangle."""
            model = create_model('X_311 = ISOTOMIC CONJUGATE OF X_54')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00311(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-00311.json"))
            write_center_svg(
                model_acute,
                here / "x-00311.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X311¶

X₃₁₁¶