← etc / Encyclopedia of Triangle Centers

X₃₀₈₁¶

DANNEELS POINT OF X₃₀

X₃₀₈₁ = reflection of X₁₆₅₀ in X₁₆₅₁

X₃₀₈₁ (DANNEELS POINT OF X₃₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3081 = DANNEELS POINT OF X_30."""

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


        def construct_x_03081(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3081 = DANNEELS POINT OF X_30 on reference triangle ABC."""
            X_1650 = point_from_barycentrics(model, A, B, C, 0.55489887, 0.47085677, -0.025755641, ID="X_1650", classes=["center"])
            X_1651 = point_from_barycentrics(model, A, B, C, 0.1117678, 0.1958099, 0.69242231, ID="X_1651", classes=["center"])
            X_3081 = reflection_in_point(model, X_1650, X_1651, ID="X_3081", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            return promote_point_to_top(model, X_3081)


        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_3081 on the given reference triangle."""
            model = create_model('X_3081 = DANNEELS POINT OF X_30')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03081(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-03081.json"))
            write_center_svg(
                model_acute,
                here / "x-03081.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3081¶

X₃₀₈₁¶