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X₃₄₈₁¶

INTERSECTION OF LINES X₃X_2120 and X₄X_2121

X₃₄₈₁ (INTERSECTION OF LINES X₃X_2120 and X₄X_2121) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3481 = INTERSECTION OF LINES X_3X_2120 and X_4X_2121."""

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


        def construct_x_03481(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3481 = INTERSECTION OF LINES X_3X_2120 and X_4X_2121 on reference triangle ABC."""
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_2120 = point_from_barycentrics(model, A, B, C, 0.30475192, 0.22664215, 0.46860594, ID="X_2120", classes=["center"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_2121 = point_from_barycentrics(model, A, B, C, 0.23747658, 0.45982126, 0.30270216, ID="X_2121", classes=["center"])
            central_line(model, X_3, X_2120, 3, 2120)
            central_line(model, X_4, X_2121, 4, 2121)
            X_3481 = intersect_lines(model, X_3, X_2120, X_4, X_2121, ID="X_3481", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_3482 = point_from_barycentrics(model, A, B, C, 0.79438361, 0.27851823, -0.072901845, ID="X_3482", classes=["center", "incident"])
            central_line(model, X_30, X_3482, 30, 3482, incident=True)
            return promote_point_to_top(model, X_3481)


        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_3481 on the given reference triangle."""
            model = create_model('X_3481 = INTERSECTION OF LINES X_3X_2120 and X_4X_2121')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03481(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-03481.json"))
            write_center_svg(
                model_acute,
                here / "x-03481.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3481¶

X₃₄₈₁¶