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X₃₆₀₀¶

INTERSECTION OF LINES X₁X_7 AND X₈X_57

X₃₆₀₀ was found by Peter Moses in connection with the 1st Liu point.

X₃₆₀₀ (INTERSECTION OF LINES X₁X_7 AND X₈X_57) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3600 = INTERSECTION OF LINES X_1X_7 AND X_8X_57."""

        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,
            incenter_of,
            nagel_point_of,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03600(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3600 = INTERSECTION OF LINES X_1X_7 AND X_8X_57 on reference triangle ABC."""
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center"])
            X_1706 = eval_trilinear_point(model, A, B, C, '(b*c*(2*(b + c) - a*(cos(A) - cos(B) - cos(C) + 1)))', ID="X_1706", classes=["center"])
            X_3600 = reflection_in_point(model, X_8, X_1706, ID="X_3600", classes=["selected", "target"], guide=False)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_1, X_7, 1, 7, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            central_line(model, X_2, X_12, 2, 12, incident=True)
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            central_line(model, X_8, X_57, 8, 57, incident=True)
            return promote_point_to_top(model, X_3600)


        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_3600 on the given reference triangle."""
            model = create_model('X_3600 = INTERSECTION OF LINES X_1X_7 AND X_8X_57')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03600(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-03600.json"))
            write_center_svg(
                model_acute,
                here / "x-03600.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3600¶

X₃₆₀₀¶