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X₃₅₃₂¶

INTERSECTION OF LINES X(6,1204) AND X(64,1620)

Let DEF be the cevian triangle of X₆₉ and A' the center of the circle that passes through D and through points where the line EF cuts to the circumcircle, and define B' and C' cyclically. The lines AA', BB', CC' concur in X₃₅₃₂. (Angel Montesdeoca, October 30, 2019)

X₃₅₃₂ (INTERSECTION OF LINES X(6,1204) AND X(64,1620)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3532 = INTERSECTION OF LINES X(6,1204) AND X(64,1620)."""

        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_trilinear_point,
            isogonal_conjugate,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03532(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3532 = INTERSECTION OF LINES X(6,1204) AND X(64,1620) on reference triangle ABC."""
            X_3146 = eval_trilinear_point(model, A, B, C, '4*cos(A) - 3*sin(B)*sin(C)', ID="X_3146", classes=["center"])
            X_3532 = isogonal_conjugate(model, A, B, C, X_3146, ID="X_3532", classes=["selected", "target"])
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center", "incident"])
            central_line(model, X_72, X_165, 72, 165, incident=True)
            X_68 = eval_trilinear_point(model, A, B, C, 'cos(A)*sec(2*A)', ID="X_68", classes=["center", "incident"])
            X_550 = eval_trilinear_point(model, A, B, C, '- cos(B - C) + 4*cos(A)', ID="X_550", classes=["center", "incident"])
            central_line(model, X_68, X_550, 68, 550, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_1192 = point_from_barycentrics(model, A, B, C, 0.1436909, 0.29955674, 0.55675236, ID="X_1192", classes=["center", "incident"])
            central_line(model, X_4, X_1192, 4, 1192, incident=True)
            return promote_point_to_top(model, X_3532)


        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_3532 on the given reference triangle."""
            model = create_model('X_3532 = INTERSECTION OF LINES X(6,1204) AND X(64,1620)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03532(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-03532.json"))
            write_center_svg(
                model_acute,
                here / "x-03532.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3532¶

X₃₅₃₂¶