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X₃₅₂₀¶

EULER LINE INTERCEPT OF LINE X₅₄X_74

X₃₅₂₀ = reflection of X₄ in X₁₅₉₄

X₃₅₂₀ (EULER LINE INTERCEPT OF LINE X₅₄X_74) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3520 = EULER LINE INTERCEPT OF LINE X_54X_74."""

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


        def construct_x_03520(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3520 = EULER LINE INTERCEPT OF LINE X_54X_74 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_1594 = eval_trilinear_point(model, A, B, C, 'sec(A) + 2*cos(B - C)', ID="X_1594", classes=["center"])
            X_3520 = reflection_in_point(model, X_4, X_1594, ID="X_3520", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_54, X_74, 54, 74, incident=True)
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_39, X_112, 39, 112, incident=True)
            return promote_point_to_top(model, X_3520)


        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_3520 on the given reference triangle."""
            model = create_model('X_3520 = EULER LINE INTERCEPT OF LINE X_54X_74')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03520(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-03520.json"))
            write_center_svg(
                model_acute,
                here / "x-03520.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3520¶

X₃₅₂₀¶