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X₂₉₆₅¶

BARYCENTRIC PRODUCT X₆₁*X₆₂

X₂₉₆₅ = crosssum of X₆ and X₂₉₃₇

X₂₉₆₅ (BARYCENTRIC PRODUCT X₆₁*X₆₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2965 = BARYCENTRIC PRODUCT X_61*X_62."""

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


        def construct_x_02965(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2965 = BARYCENTRIC PRODUCT X_61*X_62 on reference triangle ABC."""
            X_2965 = eval_trilinear_point(model, A, B, C, 'sin(A)*sin(A +  pi  /6)*sin(A -  pi  /6)', ID="X_2965", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_53 = eval_trilinear_point(model, A, B, C, 'tan(A)*cos(B - C)', ID="X_53", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_53, X_112, 53, 112, incident=True)
            X_524 = eval_trilinear_point(model, A, B, C, '(2*a**(2) - b**(2) - c**(2))/a', ID="X_524", classes=["center", "incident"])
            X_1238 = point_from_barycentrics(model, A, B, C, 0.61143196, 0.31562453, 0.072943511, ID="X_1238", classes=["center", "incident"])
            central_line(model, X_524, X_1238, 524, 1238, incident=True)
            return promote_point_to_top(model, X_2965)


        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_2965 on the given reference triangle."""
            model = create_model('X_2965 = BARYCENTRIC PRODUCT X_61*X_62')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02965(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-02965.json"))
            write_center_svg(
                model_acute,
                here / "x-02965.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2965¶

X₂₉₆₅¶