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X₃₇₃¶

CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID

X₃₇₃ is the centroid of the pedal triangle of the centroid.

X₃₇₃ (CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_373 = CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00373(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_373 = CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID on reference triangle ABC."""
            X_373 = eval_trilinear_point(model, A, B, C, '(2*b*c + a*c*cos(C) + a*b*cos(B))', ID="X_373", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            central_line(model, X_2, X_51, 2, 51, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_113 = eval_trilinear_point(model, A, B, C, 'sin(B)*sin(C)*((sin(C))/(cos(C) - 2*cos(A)*cos(B)) + (sin(B))/(cos(B) - 2*cos(A)*cos(C)))', ID="X_113", classes=["center", "incident"])
            central_line(model, X_5, X_113, 5, 113, incident=True)
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_575 = eval_trilinear_point(model, A, B, C, '3*sin(A) + cos(A)*cot(omega) ', ID="X_575", classes=["center", "incident"])
            central_line(model, X_110, X_575, 110, 575, incident=True)
            return promote_point_to_top(model, X_373)


        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_373 on the given reference triangle."""
            model = create_model('X_373 = CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00373(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-00373.json"))
            write_center_svg(
                model_acute,
                here / "x-00373.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X373¶

X₃₇₃¶