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X₃₇₄¶

CENTROID OF THE PEDAL TRIANGLE OF X₉

X₃₇₄ is the centroid of the pedal triangle of X₉.

X₃₇₄ (CENTROID OF THE PEDAL TRIANGLE OF X₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_374 = CENTROID OF THE PEDAL TRIANGLE OF X_9."""

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


        def construct_x_00374(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_374 = CENTROID OF THE PEDAL TRIANGLE OF X_9 on reference triangle ABC."""
            X_374 = eval_trilinear_point(model, A, B, C, '(2*b + 2*c - 3*a + (c + a)*cos(C) + (b + a)*cos(B))', ID="X_374", classes=["selected", "target"])
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            central_line(model, X_44, X_65, 44, 65, incident=True)
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            X_210 = eval_trilinear_point(model, A, B, C, '(b + c)*(b + c - a)', ID="X_210", classes=["center", "incident"])
            central_line(model, X_51, X_210, 51, 210, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_354 = eval_trilinear_point(model, A, B, C, '(b - c)**(2) - a*b - a*c', ID="X_354", classes=["center", "incident"])
            central_line(model, X_6, X_354, 6, 354, incident=True)
            return promote_point_to_top(model, X_374)


        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_374 on the given reference triangle."""
            model = create_model('X_374 = CENTROID OF THE PEDAL TRIANGLE OF X_9')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00374(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-00374.json"))
            write_center_svg(
                model_acute,
                here / "x-00374.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X374¶

X₃₇₄¶