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X₃₅₂₆¶

EULER LINE INTERCEPT OF LINE X₄₉X_182

X₃₅₂₆ = midpoint of X₃₀₉₀ and X₃₅₂₃

X₃₅₂₆ (EULER LINE INTERCEPT OF LINE X₄₉X_182) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3526 = EULER LINE INTERCEPT OF LINE X_49X_182."""

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


        def construct_x_03526(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3526 = EULER LINE INTERCEPT OF LINE X_49X_182 on reference triangle ABC."""
            X_3090 = eval_trilinear_point(model, A, B, C, 'sin(B)*sin(C) + cos(B - C)', ID="X_3090", classes=["center"])
            X_3523 = eval_trilinear_point(model, A, B, C, '(3*cos(A) + cos(B)*cos(C))', ID="X_3523", classes=["center"])
            X_3526 = midpoint(model, X_3090, X_3523, ID="X_3526", 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_49 = eval_trilinear_point(model, A, B, C, 'cos(3*A)', ID="X_49", classes=["center", "incident"])
            X_182 = eval_trilinear_point(model, A, B, C, 'cos(A-  omega  )', ID="X_182", classes=["center", "incident"])
            central_line(model, X_49, X_182, 49, 182, incident=True)
            X_195 = eval_trilinear_point(model, A, B, C, 'a*(a**(8) + b**(8) + c**(8) - 4*a**(6)*(b**(2) + c**(2)) + a**(4)*(6*b**(4) + 6*c**(4) + 5*b**(2)*c**(2)) - a**(2)*(4*b**(6) + 4*c**(6) - b**(4)*c**(2) - b**(2)*c**(4)) - 2*b**(2)*c**(2)*(b**(4) + c**(4) - b**(2)*c**(2)))', ID="X_195", classes=["center", "incident"])
            X_394 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A)', ID="X_394", classes=["center", "incident"])
            central_line(model, X_195, X_394, 195, 394, incident=True)
            return promote_point_to_top(model, X_3526)


        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_3526 on the given reference triangle."""
            model = create_model('X_3526 = EULER LINE INTERCEPT OF LINE X_49X_182')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03526(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-03526.json"))
            write_center_svg(
                model_acute,
                here / "x-03526.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3526¶

X₃₅₂₆¶