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X₃₅₄₃¶

EULER LINE INTERCEPT OF LINE X₁₄₆X_148

X₃₅₄₃ = midpoint of X₂ and X₃₁₄₆

X₃₅₄₃ (EULER LINE INTERCEPT OF LINE X₁₄₆X_148) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3543 = EULER LINE INTERCEPT OF LINE X_146X_148."""

        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,
            midpoint,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03543(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3543 = EULER LINE INTERCEPT OF LINE X_146X_148 on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3146 = eval_trilinear_point(model, A, B, C, '4*cos(A) - 3*sin(B)*sin(C)', ID="X_3146", classes=["center"])
            X_3543 = midpoint(model, X_2, X_3146, ID="X_3543", classes=["selected", "target"], guide=False)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_146 = eval_barycentric_point(model, A, B, C, 'a**(10) + a**(8)*(b**(2) + c**(2)) - a**(6)*(8*b**(4) - 9*b**(2)*c**(2) + 8*c**(4)) + 2*a**(4)*(b**(2) + c**(2))*(4*b**(4) - 7*b**(2)*c**(2) + 4*c**(4)) - a**(2)*(b**(2) - c**(2))**(2)*(b**(4) + 9*b**(2)*c**(2) + c**(4)) - (b**(2) - c**(2))**(4)*(b**(2) + c**(2))', ID="X_146", classes=["center", "incident"])
            X_148 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) - (b**(2) - c**(2))**(2) + b**(2)*c**(2) - a**(2)*b**(2) - a**(2)*c**(2))', ID="X_148", classes=["center", "incident"])
            central_line(model, X_146, X_148, 146, 148, incident=True)
            X_253 = eval_trilinear_point(model, A, B, C, '((csc(A))/(tan(B) + tan(C) - tan(A)))', ID="X_253", classes=["center", "incident"])
            X_317 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(2*A)*(csc(A))**(2)', ID="X_317", classes=["center", "incident"])
            central_line(model, X_253, X_317, 253, 317, incident=True)
            return promote_point_to_top(model, X_3543)


        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_3543 on the given reference triangle."""
            model = create_model('X_3543 = EULER LINE INTERCEPT OF LINE X_146X_148')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03543(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-03543.json"))
            write_center_svg(
                model_acute,
                here / "x-03543.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3543¶

X₃₅₄₃¶