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X₁₀₇₈¶

INTERSECTION OF LINES X₂X_32 AND X₃X_76

X₁₀₇₈ (INTERSECTION OF LINES X₂X_32 AND X₃X_76) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1078 = INTERSECTION OF LINES X_2X_32 AND X_3X_76."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01078(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1078 = INTERSECTION OF LINES X_2X_32 AND X_3X_76 on reference triangle ABC."""
            X_1078 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(2)*c**(2) + c**(2)*a**(2) + a**(2)*b**(2) - a**(4)))', ID="X_1078", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            central_line(model, X_2, X_32, 2, 32, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            central_line(model, X_3, X_76, 3, 76, incident=True)
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_54, X_69, 54, 69, incident=True)
            return promote_point_to_top(model, X_1078)


        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_1078 on the given reference triangle."""
            model = create_model('X_1078 = INTERSECTION OF LINES X_2X_32 AND X_3X_76')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01078(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-01078.json"))
            write_center_svg(
                model_acute,
                here / "x-01078.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1078¶

X₁₀₇₈¶