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X₃₃₃₁¶

INTERSECTION OF LINES X₄X_6 AND X₁₈₇X_237

X₃₃₃₁ = crossdifference of every pair of points on the line X₂ X₅₂₀

X₃₃₃₁ (INTERSECTION OF LINES X₄X_6 AND X₁₈₇X_237) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3331 = INTERSECTION OF LINES X_4X_6 AND X_187X_237."""

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


        def construct_x_03331(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3331 = INTERSECTION OF LINES X_4X_6 AND X_187X_237 on reference triangle ABC."""
            X_3331 = eval_trilinear_point(model, A, B, C, '((csc(B)*cos(C))*(sin(2*A) - sin(2*B)) - (csc(C)*cos(B))*(sin(2*C) - sin(2*A)))', ID="X_3331", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_4, X_6, 4, 6, incident=True)
            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_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_1625 = eval_barycentric_point(model, A, B, C, 'a**(2)*(a**(2)*(b**(2) + c**(2)) - (b**(2) - c**(2))**(2)) / (b**(2) - c**(2))', ID="X_1625", classes=["center", "incident"])
            central_line(model, X_30, X_1625, 30, 1625, incident=True)
            return promote_point_to_top(model, X_3331)


        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_3331 on the given reference triangle."""
            model = create_model('X_3331 = INTERSECTION OF LINES X_4X_6 AND X_187X_237')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03331(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-03331.json"))
            write_center_svg(
                model_acute,
                here / "x-03331.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3331¶

X₃₃₃₁¶