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X₂₆₂¶

ISOGONAL CONJUGATE OF X₁₈₂

Let P_a be the parabola with focus A and directrix BC. Let L_a be the polar of X₃ wrt P_a and define L_b and L_c cyclically. Let A' = L_b∩L_c, B' = L_c∩L_a, C' = L_a∩L_b. The lines AA', BB', CC' concur in X₂₆₂. Also, X₂₆₂ is also the isotomic conjugate, wrt A'B'C', of X₃.

X₂₆₂ (ISOGONAL CONJUGATE OF X₁₈₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_262 = ISOGONAL CONJUGATE OF X_182."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            nine_point_center_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00262(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_262 = ISOGONAL CONJUGATE OF X_182 on reference triangle ABC."""
            X_182 = eval_trilinear_point(model, A, B, C, 'cos(A-  omega  )', ID="X_182", classes=["center"])
            X_262 = isogonal_conjugate(model, A, B, C, X_182, ID="X_262", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", 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_4, X_39, 4, 39, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            central_line(model, X_2, X_51, 2, 51, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", 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_5, X_76, 5, 76, incident=True)
            return promote_point_to_top(model, X_262)


        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_262 on the given reference triangle."""
            model = create_model('X_262 = ISOGONAL CONJUGATE OF X_182')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00262(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-00262.json"))
            write_center_svg(
                model_acute,
                here / "x-00262.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X262¶

X₂₆₂¶