← etc / Encyclopedia of Triangle Centers

X₃₇₂₁¶

X₂₁₃com(INCENTRAL TRIANGLE)

X₃₇₂₁ (X₂₁₃com(INCENTRAL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3721 = X_213com(INCENTRAL 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,
            crosspoint,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03721(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3721 = X_213com(INCENTRAL TRIANGLE) on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center"])
            X_3721 = crosspoint(model, A, B, C, X_1, X_76, ID="X_3721", classes=["selected", "target"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            central_line(model, X_1, X_32, 1, 32, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            central_line(model, X_37, X_65, 37, 65, incident=True)
            X_257 = eval_trilinear_point(model, A, B, C, '1/(a**(3) + a*b*c)', ID="X_257", classes=["center", "incident"])
            X_335 = eval_trilinear_point(model, A, B, C, 'b*c/(a**(2) - b*c)', ID="X_335", classes=["center", "incident"])
            central_line(model, X_257, X_335, 257, 335, incident=True)
            return promote_point_to_top(model, X_3721)


        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_3721 on the given reference triangle."""
            model = create_model('X_3721 = X_213com(INCENTRAL TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03721(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-03721.json"))
            write_center_svg(
                model_acute,
                here / "x-03721.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3721¶

X₃₇₂₁¶