← etc / Encyclopedia of Triangle Centers

X₂₅₃₆¶

INSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE)

X₂₅₃₆ is the insimilicenter(circumcircle, Spieker radical circle).

X₂₅₃₆ (INSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2536 = INSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE)."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02536(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2536 = INSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE) on reference triangle ABC."""
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center"])
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center"])
            X_2535 = point_from_barycentrics(model, A, B, C, 0.2314987, 0.33333333, 0.43516797, ID="X_2535", classes=["center"])
            central_line(model, X_3, X_10, 3, 10)
            central_line(model, X_55, X_2535, 55, 2535)
            X_2536 = intersect_lines(model, X_3, X_10, X_55, X_2535, ID="X_2536", classes=["selected", "target"])
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_2534 = point_from_barycentrics(model, A, B, C, 0.29970374, 0.33333333, 0.36696293, ID="X_2534", classes=["center", "incident"])
            central_line(model, X_56, X_2534, 56, 2534, incident=True)
            return promote_point_to_top(model, X_2536)


        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_2536 on the given reference triangle."""
            model = create_model('X_2536 = INSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02536(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-02536.json"))
            write_center_svg(
                model_acute,
                here / "x-02536.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2536¶

X₂₅₃₆¶