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X₃₃₆₁¶

INTERSECTION OF LINES X₁X_3 AND X₇X_1125

Let O_A be the circle tangent to side BC at its midpoint and to the circumcircle on the side ob BC opposite A. Define O_B and O_C cyclically. Let A' be the insimilicanter of O_B and O_C, and define B' and C' cyclically. The lines AA', BB', CC' concur in X₃₃₆₁. See the reference at X₁₀₀₁.

X₃₃₆₁ (INTERSECTION OF LINES X₁X_3 AND X₇X_1125) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3361 = INTERSECTION OF LINES X_1X_3 AND X_7X_1125."""

        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_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03361(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3361 = INTERSECTION OF LINES X_1X_3 AND X_7X_1125 on reference triangle ABC."""
            X_3361 = eval_trilinear_point(model, A, B, C, '(3*a + b + c)/(-a + b + c)', ID="X_3361", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            central_line(model, X_1, X_3, 1, 3, incident=True)
            X_58 = eval_trilinear_point(model, A, B, C, 'a/(b + c)', ID="X_58", classes=["center", "incident"])
            X_269 = eval_trilinear_point(model, A, B, C, '(tan(A/2))**(2)', ID="X_269", classes=["center", "incident"])
            central_line(model, X_58, X_269, 58, 269, incident=True)
            X_200 = eval_trilinear_point(model, A, B, C, '(cot(A/2))**(2)', ID="X_200", classes=["center", "incident"])
            X_404 = eval_trilinear_point(model, A, B, C, '(b*c*(a + b + c) - a*(b**(2) + c**(2) - a**(2)))', ID="X_404", classes=["center", "incident"])
            central_line(model, X_200, X_404, 200, 404, incident=True)
            return promote_point_to_top(model, X_3361)


        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_3361 on the given reference triangle."""
            model = create_model('X_3361 = INTERSECTION OF LINES X_1X_3 AND X_7X_1125')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03361(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-03361.json"))
            write_center_svg(
                model_acute,
                here / "x-03361.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3361¶

X₃₃₆₁¶