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X₁₃₈¶

X₁₁₁-OF-ORTHIC-TRIANGLE

X₁₃₈ (X₁₁₁-OF-ORTHIC-TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_138 = X_111-OF-ORTHIC-TRIANGLE."""

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


        def construct_x_00138(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_138 = X_111-OF-ORTHIC-TRIANGLE on reference triangle ABC."""
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center"])
            X_130 = eval_trilinear_point(model, A, B, C, '((sin(A))*(sin(2*B) + sin(2*C))*((sin(2*B) - sin(2*C))**(2))*((sin(2*A))**(2) + sin(2*B)*sin(2*C)))', ID="X_130", classes=["center"])
            X_53 = eval_trilinear_point(model, A, B, C, 'tan(A)*cos(B - C)', ID="X_53", classes=["center"])
            X_137 = point_from_barycentrics(model, A, B, C, 0.1354431, 0.64976082, 0.21479608, ID="X_137", classes=["center"])
            central_line(model, X_51, X_130, 51, 130)
            central_line(model, X_53, X_137, 53, 137)
            X_138 = intersect_lines(model, X_51, X_130, X_53, X_137, ID="X_138", classes=["selected", "target"])
            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"])
            X_233 = eval_trilinear_point(model, A, B, C, '(b*cos(C - A) + c*cos(B - A))*cos(B - C)', ID="X_233", classes=["center", "incident"])
            central_line(model, X_122, X_233, 122, 233, incident=True)
            return promote_point_to_top(model, X_138)


        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_138 on the given reference triangle."""
            model = create_model('X_138 = X_111-OF-ORTHIC-TRIANGLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00138(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-00138.json"))
            write_center_svg(
                model_acute,
                here / "x-00138.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X138¶

X₁₃₈¶