← etc / Encyclopedia of Triangle Centers

X₃₆₆₅¶

X₄₁com(INTOUCH TRIANGLE)

X₃₆₆₅ (X₄₁com(INTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3665 = X_41com(INTOUCH 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_barycentric_point,
            eval_trilinear_point,
            gergonne_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03665(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3665 = X_41com(INTOUCH TRIANGLE) on reference triangle ABC."""
            X_3665 = eval_barycentric_point(model, A, B, C, '((b**(2) + c**(2))/(b + c - a))', ID="X_3665", classes=["selected", "target"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            central_line(model, X_7, X_21, 7, 21, incident=True)
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            X_85 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c - a)', ID="X_85", classes=["center", "incident"])
            central_line(model, X_12, X_85, 12, 85, incident=True)
            X_226 = eval_trilinear_point(model, A, B, C, '(csc(A))*(cos(B) + cos(C))', ID="X_226", classes=["center", "incident"])
            X_241 = eval_trilinear_point(model, A, B, C, '(cos(B/2))**(4) - ((cos(A/2))**(2))*((cos(B/2))**(2) +(cos(C/2))**(2)) + (cos(C/2))**(4)', ID="X_241", classes=["center", "incident"])
            central_line(model, X_226, X_241, 226, 241, incident=True)
            return promote_point_to_top(model, X_3665)


        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_3665 on the given reference triangle."""
            model = create_model('X_3665 = X_41com(INTOUCH TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03665(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-03665.json"))
            write_center_svg(
                model_acute,
                here / "x-03665.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3665¶

X₃₆₆₅¶