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X₁₃₃¶

INTERSECTION OF LINES X₄X_74 AND X₅X_122

X₁₃₃ = X₁₀₆-of-orthic triangle is ABC is acute.

X₁₃₃ (INTERSECTION OF LINES X₄X_74 AND X₅X_122) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_133 = INTERSECTION OF LINES X_4X_74 AND X_5X_122."""

        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,
            midpoint,
            nine_point_center_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00133(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_133 = INTERSECTION OF LINES X_4X_74 AND X_5X_122 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center"])
            X_133 = midpoint(model, X_4, X_107, ID="X_133", classes=["selected", "target"], guide=False)
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_4, X_74, 4, 74, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_122 = eval_trilinear_point(model, A, B, C, '(b**(2) - c**(2))**(2)*(cos(A) - cos(B)*cos(C))*(cot(A))**(2)', ID="X_122", classes=["center", "incident"])
            central_line(model, X_5, X_122, 5, 122, incident=True)
            X_53 = eval_trilinear_point(model, A, B, C, 'tan(A)*cos(B - C)', ID="X_53", classes=["center", "incident"])
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            central_line(model, X_53, X_115, 53, 115, incident=True)
            return promote_point_to_top(model, X_133)


        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_133 on the given reference triangle."""
            model = create_model('X_133 = INTERSECTION OF LINES X_4X_74 AND X_5X_122')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00133(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-00133.json"))
            write_center_svg(
                model_acute,
                here / "x-00133.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X133¶

X₁₃₃¶