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X₃₃₃₂¶

INTERSECTION OF LINES X₁X_7 AND X₄X_6

X₃₃₃₂ = crossdifference of every pair of points on the line X₅₂₀ X₆₅₇

X₃₃₃₂ (INTERSECTION OF LINES X₁X_7 AND X₄X_6) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3332 = INTERSECTION OF LINES X_1X_7 AND X_4X_6."""

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


        def construct_x_03332(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3332 = INTERSECTION OF LINES X_1X_7 AND X_4X_6 on reference triangle ABC."""
            X_3332 = eval_trilinear_point(model, A, B, C, '((cos(C))*(1 + cos(B))*(cos(C) - cos(A))*(sin(2*A) - sin(2*B)) - (cos(B))*(1 + cos(C))*(cos(A) - cos(B))*(sin(2*C) - sin(2*A)))', ID="X_3332", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_1, X_7, 1, 7, incident=True)
            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_278 = eval_trilinear_point(model, A, B, C, 'sec(A)*tan(A/2)', ID="X_278", classes=["center", "incident"])
            X_1456 = point_from_barycentrics(model, A, B, C, -0.40740741, -0.35555556, 1.762963, ID="X_1456", classes=["center", "incident"])
            central_line(model, X_278, X_1456, 278, 1456, incident=True)
            return promote_point_to_top(model, X_3332)


        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_3332 on the given reference triangle."""
            model = create_model('X_3332 = INTERSECTION OF LINES X_1X_7 AND X_4X_6')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03332(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-03332.json"))
            write_center_svg(
                model_acute,
                here / "x-03332.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3332¶

X₃₃₃₂¶