← etc / Encyclopedia of Triangle Centers

X₂₉₈₈¶

DC(X₁₀₂)

X₂₉₈₈ (DC(X₁₀₂)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2988 = DC(X_102)."""

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


        def construct_x_02988(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2988 = DC(X_102) on reference triangle ABC."""
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_515 = eval_trilinear_point(model, A, B, C, '(b + c)*sec(A) - b*sec(B) - c*sec(C)', ID="X_515", classes=["center"])
            X_2988 = cevapoint(model, A, B, C, X_6, X_515, ID="X_2988", classes=["selected", "target"])
            X_29 = eval_trilinear_point(model, A, B, C, '(sec(A))/(cos(B) + cos(C))', ID="X_29", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_29, X_110, 29, 110, incident=True)
            X_92 = eval_trilinear_point(model, A, B, C, 'csc(2*A)', ID="X_92", classes=["center", "incident"])
            X_651 = eval_trilinear_point(model, A, B, C, '1/(cos(B) - cos(C))', ID="X_651", classes=["center", "incident"])
            central_line(model, X_92, X_651, 92, 651, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_1331 = eval_trilinear_point(model, A, B, C, '(cos(A))/(b - c)', ID="X_1331", classes=["center", "incident"])
            central_line(model, X_8, X_1331, 8, 1331, incident=True)
            return promote_point_to_top(model, X_2988)


        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_2988 on the given reference triangle."""
            model = create_model('X_2988 = DC(X_102)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02988(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-02988.json"))
            write_center_svg(
                model_acute,
                here / "x-02988.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2988¶

X₂₉₈₈¶