← etc / Encyclopedia of Triangle Centers

X₃₅₁₂¶

ISOGONAL CONJUGATE OF X₃₅₀₉

X₃₅₁₂ is the isogonal conjugate of X₃₅₀₉.

X₃₅₁₂ (ISOGONAL CONJUGATE OF X₃₅₀₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3512 = ISOGONAL CONJUGATE OF X_3509."""

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


        def construct_x_03512(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3512 = ISOGONAL CONJUGATE OF X_3509 on reference triangle ABC."""
            X_3512 = eval_trilinear_point(model, A, B, C, '(1/(a**(3) - b**(3) - c**(3) + a*b*c))', ID="X_3512", classes=["selected", "target"])
            X_335 = eval_trilinear_point(model, A, B, C, 'b*c/(a**(2) - b*c)', ID="X_335", classes=["center", "incident"])
            X_385 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) - b**(2)*c**(2))', ID="X_385", classes=["center", "incident"])
            central_line(model, X_335, X_385, 335, 385, incident=True)
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            X_846 = eval_trilinear_point(model, A, B, C, '(- a**(2) + b**(2) + c**(2) + b*c + c*a + a*b)', ID="X_846", classes=["center", "incident"])
            central_line(model, X_55, X_846, 55, 846, incident=True)
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_1423 = eval_trilinear_point(model, A, B, C, '((a*b + a*c - b*c)/(b + c - a))', ID="X_1423", classes=["center", "incident"])
            central_line(model, X_19, X_1423, 19, 1423, incident=True)
            return promote_point_to_top(model, X_3512)


        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_3512 on the given reference triangle."""
            model = create_model('X_3512 = ISOGONAL CONJUGATE OF X_3509')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03512(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-03512.json"))
            write_center_svg(
                model_acute,
                here / "x-03512.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3512¶

X₃₅₁₂¶