← etc / Encyclopedia of Triangle Centers

X₁₃₄₈¶

INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE)

X₁₃₄₈ is the insimilicenter(nine-point circle, Brocard circle).

X₁₃₄₈ (INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD 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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nine_point_center_of,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01348(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) on reference triangle ABC."""
            X_1348 = eval_trilinear_point(model, A, B, C, 'e*cos(B - C) + cos(A -  omega  )', ID="X_1348", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_182 = eval_trilinear_point(model, A, B, C, 'cos(A-  omega  )', ID="X_182", classes=["center", "incident"])
            central_line(model, X_5, X_182, 5, 182, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_1341 = point_from_barycentrics(model, A, B, C, 0.30653192, 0.35355532, 0.33991277, ID="X_1341", classes=["center", "incident"])
            central_line(model, X_2, X_1341, 2, 1341, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_1340 = point_from_barycentrics(model, A, B, C, 0.34709524, 0.36700624, 0.28589852, ID="X_1340", classes=["center", "incident"])
            central_line(model, X_4, X_1340, 4, 1340, incident=True)
            return promote_point_to_top(model, X_1348)


        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_1348 on the given reference triangle."""
            model = create_model('X_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01348(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-01348.json"))
            write_center_svg(
                model_acute,
                here / "x-01348.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1348¶

X₁₃₄₈¶