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X₁₆₇₅¶

EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE)

X₁₆₇₅ is the exsimilicenter(incircle, Brocard circle).

X₁₆₇₅ (EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1675 = EXSIMILICENTER(INCIRCLE, 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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            feuerbach_point_of,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01675(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1675 = EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE) on reference triangle ABC."""
            X_1675 = eval_trilinear_point(model, A, B, C, 'e - cos(A -  omega  )', ID="X_1675", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", 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_1, X_182, 1, 182, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_1349 = eval_trilinear_point(model, A, B, C, 'e*cos(B - C) - cos(A -  omega  )', ID="X_1349", classes=["center", "incident"])
            central_line(model, X_11, X_1349, 11, 1349, incident=True)
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            X_1348 = eval_trilinear_point(model, A, B, C, 'e*cos(B - C) + cos(A -  omega  )', ID="X_1348", classes=["center", "incident"])
            central_line(model, X_12, X_1348, 12, 1348, incident=True)
            return promote_point_to_top(model, X_1675)


        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_1675 on the given reference triangle."""
            model = create_model('X_1675 = EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01675(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-01675.json"))
            write_center_svg(
                model_acute,
                here / "x-01675.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1675¶

X₁₆₇₅¶