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X₃₂₈₈¶

INTERSECTION OF LINES X₂₃₇X_351 AND X₅₂₃X_879

Let L denote the line through X₂ parallel to the Brocard axis, X₃ X₆. Coefficients for a trilinear equation for L are the trilinears for X₃₂₈₈.

X₃₂₈₈ (INTERSECTION OF LINES X₂₃₇X_351 AND X₅₂₃X_879) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3288 = INTERSECTION OF LINES X_237X_351 AND X_523X_879."""

        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,
            crosspoint,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03288(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3288 = INTERSECTION OF LINES X_237X_351 AND X_523X_879 on reference triangle ABC."""
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center"])
            X_3114 = eval_trilinear_point(model, A, B, C, '1/(a**(3)*(b**(4) + c**(4) + b**(2)*c**(2)))', ID="X_3114", classes=["center"])
            X_3288 = crosspoint(model, A, B, C, X_99, X_3114, ID="X_3288", classes=["selected", "target"])
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center", "incident"])
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            central_line(model, X_187, X_237, 187, 237, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            central_line(model, X_6, X_523, 6, 523, incident=True)
            X_323 = eval_trilinear_point(model, A, B, C, 'sin(3*A)*(csc(A))**(2)', ID="X_323", classes=["center", "incident"])
            X_401 = eval_trilinear_point(model, A, B, C, '(sin(2*B)*sin(2*C) - (sin(2*A))**(2))*(csc(A))', ID="X_401", classes=["center", "incident"])
            central_line(model, X_323, X_401, 323, 401, incident=True)
            return promote_point_to_top(model, X_3288)


        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_3288 on the given reference triangle."""
            model = create_model('X_3288 = INTERSECTION OF LINES X_237X_351 AND X_523X_879')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03288(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-03288.json"))
            write_center_svg(
                model_acute,
                here / "x-03288.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3288¶

X₃₂₈₈¶