← etc / Encyclopedia of Triangle Centers

X₃₆₄₁¶

2nd KIRIKAMI POINT

X₃₆₄₁ = X₁-of-inner-Grebe-triangle

X₃₆₄₁ (2nd KIRIKAMI POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3641 = 2nd KIRIKAMI POINT."""

        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_barycentric_point,
            eval_trilinear_point,
            incenter_of,
            nagel_point_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03641(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3641 = 2nd KIRIKAMI POINT on reference triangle ABC."""
            X_3641 = eval_barycentric_point(model, A, B, C, 'a*(b**(2) + c**(2) - a*(b + c) - S)', ID="X_3641", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_1, X_6, 1, 6, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_176 = eval_trilinear_point(model, A, B, C, '1 + sec(A/2)*cos(B/2)*cos(C/2)', ID="X_176", classes=["center", "incident"])
            central_line(model, X_8, X_176, 8, 176, incident=True)
            X_517 = eval_trilinear_point(model, A, B, C, '-1 + cos(B) + cos(C)', ID="X_517", classes=["center", "incident"])
            X_1161 = eval_trilinear_point(model, A, B, C, '(1 - 2*cot(A) - 2*cot(B) - 2*cot(C))*cos(A) + 2*sin(A)', ID="X_1161", classes=["center", "incident"])
            central_line(model, X_517, X_1161, 517, 1161, incident=True)
            return promote_point_to_top(model, X_3641)


        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_3641 on the given reference triangle."""
            model = create_model('X_3641 = 2nd KIRIKAMI POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03641(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-03641.json"))
            write_center_svg(
                model_acute,
                here / "x-03641.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3641¶

X₃₆₄₁¶