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X₁₁₁₂¶

CROSSPOINT OF X₄ AND X₂₅₀

X₁₁₁₂ is the crosspoint of X₄ and X₂₅₀.

X₁₁₁₂ (CROSSPOINT OF X₄ AND X₂₅₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1112 = CROSSPOINT OF X_4 AND X_250."""

        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,
            orthocenter_of,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01112(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1112 = CROSSPOINT OF X_4 AND X_250 on reference triangle ABC."""
            X_974 = eval_trilinear_point(model, A, B, C, '(s*a**(10) - a**(8)*(3*b**(4) - 2*b**(2)*c**(2) + 3*c**(4)) + a**(6)*s*(2*b**(4) - 3*b**(2)*c**(2) + 2*c**(4)) + a**(4)*(b**(2) - c**(2))**(2)*(2*b**(4) - 7*b**(2)*c**(2) + 2*c**(4)) - 3*a**(2)*s*(b**(2) - c**(2))**(2)*(b**(4) - 3*b**(2)*c**(2) + c**(4)) + (b**(2) - c**(2))**(4)*(b**(4) + b**(2)*c**(2) + c**(4)))*cos(A)', ID="X_974", classes=["center"])
            X_389 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(2*A)*cos(B - C)', ID="X_389", classes=["center"])
            X_1112 = reflection_in_point(model, X_974, X_389, ID="X_1112", classes=["selected", "target"], guide=False)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_94 = eval_trilinear_point(model, A, B, C, 'csc(3*A)', ID="X_94", classes=["center", "incident"])
            central_line(model, X_4, X_94, 4, 94, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_25, X_110, 25, 110, incident=True)
            X_52 = eval_trilinear_point(model, A, B, C, 'cos(2*A)*cos(B - C)', ID="X_52", classes=["center", "incident"])
            X_113 = eval_trilinear_point(model, A, B, C, 'sin(B)*sin(C)*((sin(C))/(cos(C) - 2*cos(A)*cos(B)) + (sin(B))/(cos(B) - 2*cos(A)*cos(C)))', ID="X_113", classes=["center", "incident"])
            central_line(model, X_52, X_113, 52, 113, incident=True)
            return promote_point_to_top(model, X_1112)


        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_1112 on the given reference triangle."""
            model = create_model('X_1112 = CROSSPOINT OF X_4 AND X_250')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01112(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-01112.json"))
            write_center_svg(
                model_acute,
                here / "x-01112.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1112¶

X₁₁₁₂¶