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X₂₇₈₂¶

ISOGONAL CONJUGATE OF X₂₆₉₈

As the isogonal conjugate of a point on the circumcircle, X₂₇₈₂ lies on the line at infinity.

X₂₇₈₂ (ISOGONAL CONJUGATE OF X₂₆₉₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2782 = ISOGONAL CONJUGATE OF X_2698."""

        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_trilinear_point,
            isogonal_conjugate,
            nine_point_center_of,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02782(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2782 = ISOGONAL CONJUGATE OF X_2698 on reference triangle ABC."""
            X_2698 = point_from_barycentrics(model, A, B, C, 0.78298709, -0.27279144, 0.48980435, ID="X_2698", classes=["center"])
            X_2782 = isogonal_conjugate(model, A, B, C, X_2698, ID="X_2782", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            central_line(model, X_5, X_39, 5, 39, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            central_line(model, X_3, X_76, 3, 76, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_147 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(8) + (b**(2) + c**(2))*a**(6) - (2*b**(4) + 3*b**(2)*c**(2) + 2*c**(4))*a**(4) + (b**(6) + b**(4)*c**(2) + b**(2)*c**(4) + c**(6))*a**(2) - b**(8) + b**(6)*c**(2) + b**(2)*c**(6) - c**(8))', ID="X_147", classes=["center", "incident"])
            central_line(model, X_4, X_147, 4, 147, incident=True)
            return promote_point_to_top(model, X_2782)


        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_2782 on the given reference triangle."""
            model = create_model('X_2782 = ISOGONAL CONJUGATE OF X_2698')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02782(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-02782.json"))
            write_center_svg(
                model_acute,
                here / "x-02782.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2782¶

X₂₇₈₂¶