← etc / Encyclopedia of Triangle Centers

X₃₆₉₅¶

X₅₈₀com(EXTOUCH TRIANGLE)

X₃₆₉₅ = excentral-to-ABC barycentric image of X₅₈₀

X₃₆₉₅ (X₅₈₀com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3695 = X_580com(EXTOUCH 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            nine_point_center_of,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03695(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3695 = X_580com(EXTOUCH TRIANGLE) on reference triangle ABC."""
            X_3695 = eval_barycentric_point(model, A, B, C, '((b + c)**(2)*(b**(2) + c **(2) - a**(2)))', ID="X_3695", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            central_line(model, X_10, X_37, 10, 37, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_312 = eval_trilinear_point(model, A, B, C, '(b + c - a)*b**(2)*c**(2)', ID="X_312", classes=["center", "incident"])
            central_line(model, X_5, X_312, 5, 312, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_345 = eval_trilinear_point(model, A, B, C, '(csc(A))/(1 - sec(A))', ID="X_345", classes=["center", "incident"])
            central_line(model, X_3, X_345, 3, 345, incident=True)
            return promote_point_to_top(model, X_3695)


        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_3695 on the given reference triangle."""
            model = create_model('X_3695 = X_580com(EXTOUCH TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03695(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-03695.json"))
            write_center_svg(
                model_acute,
                here / "x-03695.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3695¶

X₃₆₉₅¶