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X₃₅₄₅¶

EULER LINE INTERCEPT OF LINE X₁₁X_1056

X₃₅₄₅ = midpoint of X₄ and X₃₅₂₄

X₃₅₄₅ (EULER LINE INTERCEPT OF LINE X₁₁X_1056) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3545 = EULER LINE INTERCEPT OF LINE X_11X_1056."""

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


        def construct_x_03545(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3545 = EULER LINE INTERCEPT OF LINE X_11X_1056 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_3524 = eval_trilinear_point(model, A, B, C, '3*cos(A) + sin(B)*sin(C)', ID="X_3524", classes=["center"])
            X_3545 = midpoint(model, X_4, X_3524, ID="X_3545", 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_114 = eval_trilinear_point(model, A, B, C, 'b*c*(b*sec(B +  omega  ) + c*sec(C +  omega  ))', ID="X_114", classes=["center", "incident"])
            X_671 = eval_trilinear_point(model, A, B, C, '1/(a*(2*a**(2) - b**(2) - c**(2)))', ID="X_671", classes=["center", "incident"])
            central_line(model, X_114, X_671, 114, 671, incident=True)
            X_262 = eval_trilinear_point(model, A, B, C, 'sec(A -  omega  )', ID="X_262", classes=["center", "incident"])
            X_538 = point_from_barycentrics(model, A, B, C, -0.75777793, 0.11558409, 0.64219384, ID="X_538", classes=["center", "incident"])
            central_line(model, X_262, X_538, 262, 538, incident=True)
            return promote_point_to_top(model, X_3545)


        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_3545 on the given reference triangle."""
            model = create_model('X_3545 = EULER LINE INTERCEPT OF LINE X_11X_1056')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03545(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-03545.json"))
            write_center_svg(
                model_acute,
                here / "x-03545.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3545¶

X₃₅₄₅¶