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X₃₂₄₅¶

REFLECTION OF X₁ IN ITS TRILINEAR POLAR

X₃₂₄₅ is the reflection of X₁ in its trilinear polar.

X₃₂₄₅ (REFLECTION OF X₁ IN ITS TRILINEAR POLAR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3245 = REFLECTION OF X_1 IN ITS TRILINEAR POLAR."""

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


        def construct_x_03245(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3245 = REFLECTION OF X_1 IN ITS TRILINEAR POLAR on reference triangle ABC."""
            X_3245 = eval_trilinear_point(model, A, B, C, '2*b**(3) + 2*c**(3) - a**(3) - 2*(b + c)*(a**(2) + b*c) + a*(b**(2) + c**(2) + 3*b*c)', ID="X_3245", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            central_line(model, X_1, X_3, 1, 3, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_535 = point_from_barycentrics(model, A, B, C, -0.5703697, -0.22078827, 0.79115797, ID="X_535", classes=["center", "incident"])
            central_line(model, X_8, X_535, 8, 535, incident=True)
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            X_516 = eval_trilinear_point(model, A, B, C, 'b*c*((a - b)*cot(C) + (a - c)*cot(B))', ID="X_516", classes=["center", "incident"])
            central_line(model, X_80, X_516, 80, 516, incident=True)
            return promote_point_to_top(model, X_3245)


        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_3245 on the given reference triangle."""
            model = create_model('X_3245 = REFLECTION OF X_1 IN ITS TRILINEAR POLAR')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03245(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-03245.json"))
            write_center_svg(
                model_acute,
                here / "x-03245.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3245¶

X₃₂₄₅¶