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X₁₆₄¶

INCENTER OF EXCENTRAL TRIANGLE

X₁₆₄ is the incenter of excentral triangle.

X₁₆₄ (INCENTER OF EXCENTRAL TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_164 = INCENTER OF EXCENTRAL TRIANGLE."""

        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,
            mittenpunkt_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00164(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_164 = INCENTER OF EXCENTRAL TRIANGLE on reference triangle ABC."""
            X_164 = eval_trilinear_point(model, A, B, C, 'sin(B/2) + sin(C/2) - sin(A/2)', ID="X_164", classes=["selected", "target"])
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_168 = eval_trilinear_point(model, A, B, C, 'sin(A) - sin(B) - sin(C) + 2*(cos(A/2) + sin(B/2 - A/2) + sin(C/2 - A/2))', ID="X_168", classes=["center", "incident"])
            central_line(model, X_9, X_168, 9, 168, incident=True)
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_188 = eval_trilinear_point(model, A, B, C, 'csc(A/2)', ID="X_188", classes=["center", "incident"])
            central_line(model, X_40, X_188, 40, 188, incident=True)
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            X_177 = eval_trilinear_point(model, A, B, C, '(cos(B/2) + cos(C/2))*sec(A/2)', ID="X_177", classes=["center", "incident"])
            central_line(model, X_57, X_177, 57, 177, incident=True)
            return promote_point_to_top(model, X_164)


        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_164 on the given reference triangle."""
            model = create_model('X_164 = INCENTER OF EXCENTRAL TRIANGLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00164(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-00164.json"))
            write_center_svg(
                model_acute,
                here / "x-00164.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X164¶

X₁₆₄¶