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X₃₅₇₅¶

EULER LINE INTERCEPT OF THE LINE X₆₄X_66

X₃₅₇₅ = reflection of X₁₈₈₅ in X₄

X₃₅₇₅ (EULER LINE INTERCEPT OF THE LINE X₆₄X_66) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3575 = EULER LINE INTERCEPT OF THE LINE X_64X_66."""

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


        def construct_x_03575(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3575 = EULER LINE INTERCEPT OF THE LINE X_64X_66 on reference triangle ABC."""
            X_1885 = eval_barycentric_point(model, A, B, C, '(2*a**(6) - 3*a**(4)*(b**(2) + c**(2)) + 8*a**(2)*b**(2)*c**(2) + (b**(2) - c**(2))**(2)*(b**(2) + c**(2))) / (b**(2) + c**(2) - a**(2))', ID="X_1885", classes=["center"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_3575 = reflection_in_point(model, X_1885, X_4, ID="X_3575", 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_64 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - cos(B)*cos(C))', ID="X_64", classes=["center", "incident"])
            X_66 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4))', ID="X_66", classes=["center", "incident"])
            central_line(model, X_64, X_66, 64, 66, incident=True)
            X_128 = eval_trilinear_point(model, A, B, C, '((sec(A))*(cos(2*B) + cos(2*C))*(1 + 2*cos(2*A))*(cos(2*A) + 2*cos(2*B)*cos(2*C)))', ID="X_128", classes=["center", "incident"])
            X_135 = eval_trilinear_point(model, A, B, C, '(sec(A))*((sin(2*B))/(sec(2*C) - sec(2*A)) + (sin(2*C))/(sec(2*A) - sec(2*B)))', ID="X_135", classes=["center", "incident"])
            central_line(model, X_128, X_135, 128, 135, incident=True)
            return promote_point_to_top(model, X_3575)


        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_3575 on the given reference triangle."""
            model = create_model('X_3575 = EULER LINE INTERCEPT OF THE LINE X_64X_66')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03575(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-03575.json"))
            write_center_svg(
                model_acute,
                here / "x-03575.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3575¶

X₃₅₇₅¶