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X₃₇₅¶

CENTROID OF THE PEDAL TRIANGLE OF X₁₀

X₃₇₅ is the centroid of the pedal triangle of X₁₀.

X₃₇₅ (CENTROID OF THE PEDAL TRIANGLE OF X₁₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_375 = CENTROID OF THE PEDAL TRIANGLE OF X_10."""

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


        def construct_x_00375(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_375 = CENTROID OF THE PEDAL TRIANGLE OF X_10 on reference triangle ABC."""
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center"])
            X_210 = eval_trilinear_point(model, A, B, C, '(b + c)*(b + c - a)', ID="X_210", classes=["center"])
            X_375 = midpoint(model, X_51, X_210, ID="X_375", classes=["selected", "target"], guide=False)
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_181 = eval_trilinear_point(model, A, B, C, 'a*(b + c)**(2)/(b + c - a)', ID="X_181", classes=["center", "incident"])
            central_line(model, X_44, X_181, 44, 181, incident=True)
            central_line(model, X_51, X_210, 51, 210, incident=True)
            X_354 = eval_trilinear_point(model, A, B, C, '(b - c)**(2) - a*b - a*c', ID="X_354", classes=["center", "incident"])
            X_373 = eval_trilinear_point(model, A, B, C, '(2*b*c + a*c*cos(C) + a*b*cos(B))', ID="X_373", classes=["center", "incident"])
            central_line(model, X_354, X_373, 354, 373, incident=True)
            return promote_point_to_top(model, X_375)


        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_375 on the given reference triangle."""
            model = create_model('X_375 = CENTROID OF THE PEDAL TRIANGLE OF X_10')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00375(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-00375.json"))
            write_center_svg(
                model_acute,
                here / "x-00375.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X375¶

X₃₇₅¶