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X₃₇₆¶

CENTROID OF THE ANTIPEDAL TRIANGLE OF X₂

X₃₇₆ is the centroid of the antipedal triangle of X₂.

X₃₇₆ (CENTROID OF THE ANTIPEDAL TRIANGLE OF X₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X_2."""

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


        def construct_x_00376(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X_2 on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center"])
            X_376 = midpoint(model, X_2, X_20, ID="X_376", classes=["selected", "target"], guide=False)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_69, X_74, 69, 74, incident=True)
            X_35 = eval_trilinear_point(model, A, B, C, '1 + 2*cos(A)', ID="X_35", classes=["center", "incident"])
            X_388 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2) + (b + c)**(2))/(b + c - a)', ID="X_388", classes=["center", "incident"])
            central_line(model, X_35, X_388, 35, 388, incident=True)
            return promote_point_to_top(model, X_376)


        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_376 on the given reference triangle."""
            model = create_model('X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X_2')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00376(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-00376.json"))
            write_center_svg(
                model_acute,
                here / "x-00376.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X376¶

X₃₇₆¶