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X₃₇₇₅¶

X₅₉₄com[INVERSE(nT(bc, c²))]

X₃₇₇₅ = reflection of X₁₁₀₀ in X₁₁₂₅

X₃₇₇₅ (X₅₉₄com[INVERSE(nT(bc, c²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3775 = X_594com[INVERSE(nT(bc, c²))]."""

        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,
            incenter_of,
            promote_point_to_top,
            reflection_in_point,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03775(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3775 = X_594com[INVERSE(nT(bc, c²))] on reference triangle ABC."""
            X_1100 = eval_trilinear_point(model, A, B, C, '2*a + b + c', ID="X_1100", classes=["center"])
            X_1125 = eval_trilinear_point(model, A, B, C, '(2*a+b+c)/a', ID="X_1125", classes=["center"])
            X_3775 = reflection_in_point(model, X_1100, X_1125, ID="X_3775", classes=["selected", "target"], guide=False)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center", "incident"])
            central_line(model, X_10, X_141, 10, 141, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_319 = eval_trilinear_point(model, A, B, C, '(1 + 2*cos(A))/a**(2)', ID="X_319", classes=["center", "incident"])
            central_line(model, X_1, X_319, 1, 319, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_1211 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c)*(b**(2) + c**(2) + a*b + a*c))', ID="X_1211", classes=["center", "incident"])
            central_line(model, X_11, X_1211, 11, 1211, incident=True)
            return promote_point_to_top(model, X_3775)


        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_3775 on the given reference triangle."""
            model = create_model('X_3775 = X_594com[INVERSE(nT(bc, c²))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03775(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-03775.json"))
            write_center_svg(
                model_acute,
                here / "x-03775.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3775¶

X₃₇₇₅¶