← etc / Encyclopedia of Triangle Centers

X₂₃₂₆¶

X₂-ISOCONJUGATE OF X₁₄₂₅

X₂₃₂₆ (X₂-ISOCONJUGATE OF X₁₄₂₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2326 = X_2-ISOCONJUGATE OF X_1425."""

        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,
            cevapoint,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02326(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2326 = X_2-ISOCONJUGATE OF X_1425 on reference triangle ABC."""
            X_284 = eval_trilinear_point(model, A, B, C, '(sin(A))/(cos(B) + cos(C))', ID="X_284", classes=["center"])
            X_1172 = point_from_barycentrics(model, A, B, C, 0.14979394, 0.23060383, 0.61960222, ID="X_1172", classes=["center"])
            X_2326 = cevapoint(model, A, B, C, X_284, X_1172, ID="X_2326", classes=["selected", "target"])
            X_27 = eval_trilinear_point(model, A, B, C, '(sec(A))/(b + c)', ID="X_27", classes=["center", "incident"])
            X_86 = eval_trilinear_point(model, A, B, C, 'b*c/(b + c)', ID="X_86", classes=["center", "incident"])
            central_line(model, X_27, X_86, 27, 86, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_162 = eval_trilinear_point(model, A, B, C, '1/(sin(2*B) - sin(2*C))', ID="X_162", classes=["center", "incident"])
            central_line(model, X_6, X_162, 6, 162, incident=True)
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_270 = eval_trilinear_point(model, A, B, C, '(sec(A))/(1 + cos(B - C))', ID="X_270", classes=["center", "incident"])
            central_line(model, X_21, X_270, 21, 270, incident=True)
            return promote_point_to_top(model, X_2326)


        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_2326 on the given reference triangle."""
            model = create_model('X_2326 = X_2-ISOCONJUGATE OF X_1425')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02326(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-02326.json"))
            write_center_svg(
                model_acute,
                here / "x-02326.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2326¶

X₂₃₂₆¶