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X₃₉₁₃¶

X₁₀com[INVERSE(n(INTOUCH TRIANGLE))]

Let O_A be the circle tangent to side BC at its midpoint and to the circumcircle on the same side of BC as A. Define O_B and O_C cyclically. X₃₉₁₃ is the radical center of the circles O_A, O_B, O_C. See the reference at X₁₀₀₁.

X₃₉₁₃ (X₁₀com[INVERSE(n(INTOUCH TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3913 = X_10com[INVERSE(n(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,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03913(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3913 = X_10com[INVERSE(n(INTOUCH TRIANGLE))] on reference triangle ABC."""
            X_3913 = eval_barycentric_point(model, A, B, C, '(a*(b + c - a)*(a**(2) + a*b + a*c - 2*b*c))', ID="X_3913", classes=["selected", "target"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", 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_8, X_21, 8, 21, incident=True)
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            central_line(model, X_56, X_100, 56, 100, incident=True)
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            X_224 = eval_trilinear_point(model, A, B, C, '(cot(B)*(cos(B/2))**(2) + cot(C)*(cos(C/2))**(2) - cot(A)*(cos(A/2))**(2))*cot(A)', ID="X_224", classes=["center", "incident"])
            central_line(model, X_65, X_224, 65, 224, incident=True)
            return promote_point_to_top(model, X_3913)


        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_3913 on the given reference triangle."""
            model = create_model('X_3913 = X_10com[INVERSE(n(INTOUCH TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03913(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-03913.json"))
            write_center_svg(
                model_acute,
                here / "x-03913.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3913¶

X₃₉₁₃¶