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X₃₁₀₉¶

ORTHOGONAL PROJECTION OF X₁ ON EULER LINE

X₃₁₀₉ = orthogonal projection of X₁ on Euler line

X₃₁₀₉ (ORTHOGONAL PROJECTION OF X₁ ON EULER LINE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3109 = ORTHOGONAL PROJECTION OF X_1 ON EULER LINE."""

        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,
            feuerbach_point_of,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03109(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3109 = ORTHOGONAL PROJECTION OF X_1 ON EULER LINE on reference triangle ABC."""
            X_3109 = eval_barycentric_point(model, A, B, C, '(a + b) * (a + c) * (2*a**(5) - 2*a**(4)*b + a**(2)*b**(3) - 2*a*b**(4) + b**(5) - 2*a**(4)*c + 2*a**(3)*b*c - a**(2)*b**(2)*c + b**(4)*c - a**(2)*b*c**(2) + 4*a*b**(2)*c**(2) - 2*b**(3)*c**(2) + a**(2)*c**(3) - 2*b**(2)*c**(3) - 2*a*c**(4) + b*c**(4) + c**(5))', ID="X_3109", classes=["selected", "target"])
            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_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            central_line(model, X_1, X_523, 1, 523, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_759 = eval_trilinear_point(model, A, B, C, '(1/(a**(0)*(b**(3) + c**(3)) - a**(2)*(b**(1) + c**(1))))', ID="X_759", classes=["center", "incident"])
            central_line(model, X_11, X_759, 11, 759, incident=True)
            return promote_point_to_top(model, X_3109)


        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_3109 on the given reference triangle."""
            model = create_model('X_3109 = ORTHOGONAL PROJECTION OF X_1 ON EULER LINE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03109(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-03109.json"))
            write_center_svg(
                model_acute,
                here / "x-03109.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3109¶

X₃₁₀₉¶