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X₁₅₂¶

REFLECTION OF X₂₀ IN X₁₀₁

X₁₅₂ is the reflection of X₂₀ in X₁₀₁.

X₁₅₂ (REFLECTION OF X₂₀ IN X₁₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_152 = REFLECTION OF X_20 IN X_101."""

        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_barycentric_point,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00152(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_152 = REFLECTION OF X_20 IN X_101 on reference triangle ABC."""
            X_152 = eval_barycentric_point(model, A, B, C, 'a**(8) - a**(7)*(b + c) + a**(6)*(2*b**(2) + b*c + 2*c**(2)) - a**(5)*(5*b**(3) - b**(2)*c - b*c**(2) + 5*c**(3)) - a**(4)*b*c*(b**(2) - 6*b*c + c**(2)) + a**(3)*(5*b**(5) + b**(4)*c - 6*b**(3)*c**(2) - 6*b**(2)*c**(3) + b*c**(4) + 5*c**(5)) - a**(2)*(2*b**(6) + b**(5)*c + 2*b**(4)*c**(2) - 10*b**(3)*c**(3) + 2*b**(2)*c**(4) + b*c**(5) + 2*c**(6)) + a*(b**(7) - b**(6)*c - 3*b**(5)*c**(2) + 3*b**(4)*c**(3) + 3*b**(3)*c**(4) - 3*b**(2)*c**(5) - b*c**(6) + c**(7)) - b**(8) + b**(7)*c + 2*b**(6)*c**(2) - b**(5)*c**(3) - 2*b**(4)*c**(4) - b**(3)*c**(5) + 2*b**(2)*c**(6) + b*c**(7) - c**(8)', ID="X_152", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", 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_2, X_103, 2, 103, incident=True)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_20, X_101, 20, 101, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_150 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(4) + c**(4) - a**(4) + a*(b*c**(2) +c*b**(2) - b**(3) - c**(3)) - b*c*(a**(2) + b**(2) + c**(2)) + (b + c)*a**(3)))', ID="X_150", classes=["center", "incident"])
            central_line(model, X_4, X_150, 4, 150, incident=True)
            return promote_point_to_top(model, X_152)


        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_152 on the given reference triangle."""
            model = create_model('X_152 = REFLECTION OF X_20 IN X_101')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00152(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-00152.json"))
            write_center_svg(
                model_acute,
                here / "x-00152.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X152¶

X₁₅₂¶