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X₃₀₈₇¶

INTERSECTION OF LINES X₂X_95 AND X₄X_6

Let A'B'C' be the anti-Euler triangle. X₃₀₈₇ is the radical center of the circumcircles of triangles A'BC, B'CA, C'AB. (Randy Hutson, June 7, 2019)

X₃₀₈₇ (INTERSECTION OF LINES X₂X_95 AND X₄X_6) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3087 = INTERSECTION OF LINES X_2X_95 AND X_4X_6."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03087(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3087 = INTERSECTION OF LINES X_2X_95 AND X_4X_6 on reference triangle ABC."""
            X_3087 = eval_barycentric_point(model, A, B, C, 'tan(A) + cot(B) + cot(C)', ID="X_3087", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_4, X_6, 4, 6, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_95 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*sec(B - C)', ID="X_95", classes=["center", "incident"])
            central_line(model, X_2, X_95, 2, 95, incident=True)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_216 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*cos(B - C)', ID="X_216", classes=["center", "incident"])
            central_line(model, X_20, X_216, 20, 216, incident=True)
            return promote_point_to_top(model, X_3087)


        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_3087 on the given reference triangle."""
            model = create_model('X_3087 = INTERSECTION OF LINES X_2X_95 AND X_4X_6')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03087(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-03087.json"))
            write_center_svg(
                model_acute,
                here / "x-03087.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3087¶

X₃₀₈₇¶