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X₃₉₉¶

PARRY REFLECTION POINT

Let L, M, N be lines through A, B, C, respectively, parallel to the Euler line. Let L' be the reflection of L in sideline BC, let M' be the reflection of M in sideline CA, and let N' be the reflection of N in sideline AB. The lines L', M', N' concur in X₃₉₉, as proved in

X₃₉₉ (PARRY REFLECTION POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_399 = PARRY REFLECTION POINT."""

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


        def construct_x_00399(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_399 = PARRY REFLECTION POINT on reference triangle ABC."""
            X_399 = eval_trilinear_point(model, A, B, C, '5*cos(A) - 4*cos(B)*cos(C) - 8*sin(B)*sin(C)*(cos(A))**(2)', ID="X_399", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_13 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /3)', ID="X_13", classes=["center", "incident"])
            central_line(model, X_6, X_13, 6, 13, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_3, X_74, 3, 74, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_146 = eval_barycentric_point(model, A, B, C, 'a**(10) + a**(8)*(b**(2) + c**(2)) - a**(6)*(8*b**(4) - 9*b**(2)*c**(2) + 8*c**(4)) + 2*a**(4)*(b**(2) + c**(2))*(4*b**(4) - 7*b**(2)*c**(2) + 4*c**(4)) - a**(2)*(b**(2) - c**(2))**(2)*(b**(4) + 9*b**(2)*c**(2) + c**(4)) - (b**(2) - c**(2))**(4)*(b**(2) + c**(2))', ID="X_146", classes=["center", "incident"])
            central_line(model, X_30, X_146, 30, 146, incident=True)
            return promote_point_to_top(model, X_399)


        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_399 on the given reference triangle."""
            model = create_model('X_399 = PARRY REFLECTION POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00399(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-00399.json"))
            write_center_svg(
                model_acute,
                here / "x-00399.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X399¶

X₃₉₉¶