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X₂₉₃₆¶

TANGENTIAL-ISOGONAL CONJUGATE OF X₁₈₇

X₂₉₃₆ is the tangential-isogonal conjugate of X₁₈₇.

X₂₉₃₆ (TANGENTIAL-ISOGONAL CONJUGATE OF X₁₈₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2936 = TANGENTIAL-ISOGONAL CONJUGATE OF X_187."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02936(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2936 = TANGENTIAL-ISOGONAL CONJUGATE OF X_187 on reference triangle ABC."""
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_67 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_67", classes=["center"])
            X_22 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4))', ID="X_22", classes=["center"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center"])
            central_line(model, X_3, X_67, 3, 67)
            central_line(model, X_22, X_99, 22, 99)
            X_2936 = intersect_lines(model, X_3, X_67, X_22, X_99, ID="X_2936", classes=["selected", "target"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_543 = eval_barycentric_point(model, A, B, C, '2*a**(4) - b**(4) - c**(4) - 2*a**(2)*b**(2) - 2*a**(2)*c**(2) + 4*b**(2)*c**(2)', ID="X_543", classes=["center", "incident"])
            central_line(model, X_25, X_543, 25, 543, incident=True)
            return promote_point_to_top(model, X_2936)


        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_2936 on the given reference triangle."""
            model = create_model('X_2936 = TANGENTIAL-ISOGONAL CONJUGATE OF X_187')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02936(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-02936.json"))
            write_center_svg(
                model_acute,
                here / "x-02936.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2936¶

X₂₉₃₆¶