← etc / Encyclopedia of Triangle Centers

X₂₀₀₄¶

ORTHOCORRESPONDENT OF X₆₁

X₂₀₀₄ (ORTHOCORRESPONDENT OF X₆₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2004 = ORTHOCORRESPONDENT OF X_61."""

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


        def construct_x_02004(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2004 = ORTHOCORRESPONDENT OF X_61 on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_13 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /3)', ID="X_13", classes=["center"])
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center"])
            X_61 = eval_trilinear_point(model, A, B, C, 'sin(A +  pi  /6)', ID="X_61", classes=["center"])
            central_line(model, X_2, X_13, 2, 13)
            central_line(model, X_51, X_61, 51, 61)
            X_2004 = intersect_lines(model, X_2, X_13, X_51, X_61, ID="X_2004", classes=["selected", "target"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            X_2005 = point_from_barycentrics(model, A, B, C, 0.35631767, 0.24069977, 0.40298257, ID="X_2005", classes=["center", "incident"])
            central_line(model, X_32, X_2005, 32, 2005, incident=True)
            return promote_point_to_top(model, X_2004)


        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_2004 on the given reference triangle."""
            model = create_model('X_2004 = ORTHOCORRESPONDENT OF X_61')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02004(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-02004.json"))
            write_center_svg(
                model_acute,
                here / "x-02004.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2004¶

X₂₀₀₄¶