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X₃₂₅₄¶

REFLECTION OF X₉ IN X₁₁

X₃₂₅₄ is the reflection of X₉ in X₁₁.

X₃₂₅₄ (REFLECTION OF X₉ IN X₁₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3254 = REFLECTION OF X_9 IN X_11."""

        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,
            feuerbach_point_of,
            gergonne_point_of,
            midpoint,
            mittenpunkt_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03254(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3254 = REFLECTION OF X_9 IN X_11 on reference triangle ABC."""
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center"])
            X_149 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(3) + c**(3) - a**(3) + (a**(2) - b*c)*(b + c) + a*(b*c - b**(2) - c**(2))))', ID="X_149", classes=["center"])
            X_3254 = midpoint(model, X_7, X_149, ID="X_3254", classes=["selected", "target"], guide=False)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            central_line(model, X_9, X_11, 9, 11, incident=True)
            central_line(model, X_7, X_149, 7, 149, incident=True)
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_142 = eval_trilinear_point(model, A, B, C, 'b + c - ((b - c)**(2))/a', ID="X_142", classes=["center", "incident"])
            central_line(model, X_100, X_142, 100, 142, incident=True)
            return promote_point_to_top(model, X_3254)


        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_3254 on the given reference triangle."""
            model = create_model('X_3254 = REFLECTION OF X_9 IN X_11')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03254(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-03254.json"))
            write_center_svg(
                model_acute,
                here / "x-03254.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3254¶

X₃₂₅₄¶