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X₁₃₅¶

INTERSECTION OF LINE X₄X_131 AND X₂₅X_114

X₁₃₅ = X₁₀₈-of-orthic-triangle if ABC is acute

X₁₃₅ (INTERSECTION OF LINE X₄X_131 AND X₂₅X_114) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_135 = INTERSECTION OF LINE X_4X_131 AND X_25X_114."""

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


        def construct_x_00135(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_135 = INTERSECTION OF LINE X_4X_131 AND X_25X_114 on reference triangle ABC."""
            X_135 = eval_trilinear_point(model, A, B, C, '(sec(A))*((sin(2*B))/(sec(2*C) - sec(2*A)) + (sin(2*C))/(sec(2*A) - sec(2*B)))', ID="X_135", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_131 = point_from_barycentrics(model, A, B, C, 0.57236082, 0.12379803, 0.30384114, ID="X_131", classes=["center", "incident"])
            central_line(model, X_4, X_131, 4, 131, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_114 = eval_trilinear_point(model, A, B, C, 'b*c*(b*sec(B +  omega  ) + c*sec(C +  omega  ))', ID="X_114", classes=["center", "incident"])
            central_line(model, X_25, X_114, 25, 114, 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_135)


        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_135 on the given reference triangle."""
            model = create_model('X_135 = INTERSECTION OF LINE X_4X_131 AND X_25X_114')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00135(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-00135.json"))
            write_center_svg(
                model_acute,
                here / "x-00135.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X135¶

X₁₃₅¶