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X₂₇₈₄¶

ISOGONAL CONJUGATE OF X₂₇₀₀

X₂₇₈₄ is the isogonal conjugate of X₂₇₀₀.

X₂₇₈₄ (ISOGONAL CONJUGATE OF X₂₇₀₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2784 = ISOGONAL CONJUGATE OF X_2700."""

        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,
            incenter_of,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02784(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2784 = ISOGONAL CONJUGATE OF X_2700 on reference triangle ABC."""
            X_2700 = point_from_barycentrics(model, A, B, C, 0.90414101, -0.16964973, 0.26550872, ID="X_2700", classes=["center"])
            X_2784 = isogonal_conjugate(model, A, B, C, X_2700, ID="X_2784", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            central_line(model, X_10, X_98, 10, 98, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", 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_1, X_147, 1, 147, incident=True)
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", classes=["center", "incident"])
            central_line(model, X_99, X_103, 99, 103, incident=True)
            return promote_point_to_top(model, X_2784)


        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_2784 on the given reference triangle."""
            model = create_model('X_2784 = ISOGONAL CONJUGATE OF X_2700')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02784(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-02784.json"))
            write_center_svg(
                model_acute,
                here / "x-02784.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2784¶

X₂₇₈₄¶