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X₅₆₅¶

INTERSECTION OF LINES X₄₉X_93 AND X(143,324)

Clark Kimberling and Cyril Parry, “Products, Square Roots, and Layers in Triangle Geometry,” Mathematics and Informatics Quarterly 10 (2000) 9-22; on page 21, section 8.

X₅₆₅ (INTERSECTION OF LINES X₄₉X_93 AND X(143,324)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_565 = INTERSECTION OF LINES X_49X_93 AND X(143,324)."""

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


        def construct_x_00565(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_565 = INTERSECTION OF LINES X_49X_93 AND X(143,324) on reference triangle ABC."""
            X_565 = eval_trilinear_point(model, A, B, C, 'cos(3*B - 3*C)', ID="X_565", classes=["selected", "target"])
            X_49 = eval_trilinear_point(model, A, B, C, 'cos(3*A)', ID="X_49", classes=["center", "incident"])
            X_93 = eval_trilinear_point(model, A, B, C, 'sec(3*A)', ID="X_93", classes=["center", "incident"])
            central_line(model, X_49, X_93, 49, 93, incident=True)
            X_143 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(2*C - 2*A) + cos(2*A - 2*B))', ID="X_143", classes=["center", "incident"])
            X_324 = eval_trilinear_point(model, A, B, C, 'b*c*sec(A)*cos(B - C)', ID="X_324", classes=["center", "incident"])
            central_line(model, X_143, X_324, 143, 324, incident=True)
            return promote_point_to_top(model, X_565)


        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_565 on the given reference triangle."""
            model = create_model('X_565 = INTERSECTION OF LINES X_49X_93 AND X(143,324)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00565(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-00565.json"))
            write_center_svg(
                model_acute,
                here / "x-00565.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X565¶

X₅₆₅¶