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X₁₀₂₅¶

INTERSECTION OF LINES X₂X_7 AND X₁₀₀X_109

X₁₀₂₅ = trilinear pole of line X₂₄₁ X₅₁₈

X₁₀₂₅ (INTERSECTION OF LINES X₂X_7 AND X₁₀₀X_109) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1025 = INTERSECTION OF LINES X_2X_7 AND X_100X_109."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            gergonne_point_of,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01025(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1025 = INTERSECTION OF LINES X_2X_7 AND X_100X_109 on reference triangle ABC."""
            X_1024 = eval_trilinear_point(model, A, B, C, '((b - c)*(b + c - a)/(b**(2) + c**(2) - a*(b + c)))', ID="X_1024", classes=["center"])
            X_1025 = isogonal_conjugate(model, A, B, C, X_1024, ID="X_1025", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_2, X_7, 2, 7, incident=True)
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            central_line(model, X_100, X_109, 100, 109, incident=True)
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            X_658 = eval_trilinear_point(model, A, B, C, '1/((1 + cos(A))*(cos(B) - cos(C)))', ID="X_658", classes=["center", "incident"])
            central_line(model, X_190, X_658, 190, 658, incident=True)
            return promote_point_to_top(model, X_1025)


        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_1025 on the given reference triangle."""
            model = create_model('X_1025 = INTERSECTION OF LINES X_2X_7 AND X_100X_109')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01025(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-01025.json"))
            write_center_svg(
                model_acute,
                here / "x-01025.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1025¶

X₁₀₂₅¶