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X₃₅₇₆¶

INTERSECTION OF LINES X₁X_3 AND X₂X_515

Let P_a be the parabola with focus A and directrix BC, and define P_b and P_c cyclically. X₃₅₇₆ is the centroid of the six points of tangency of lines from X₁ to P_a, P_b, and P_c. (Randy Hutson, December 2, 2017)

X₃₅₇₆ (INTERSECTION OF LINES X₁X_3 AND X₂X_515) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3576 = INTERSECTION OF LINES X_1X_3 AND X_2X_515."""

        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,
            midpoint,
            mittenpunkt_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03576(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3576 = INTERSECTION OF LINES X_1X_3 AND X_2X_515 on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center"])
            X_3576 = midpoint(model, X_1, X_165, ID="X_3576", classes=["selected", "target"], guide=False)
            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_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            central_line(model, X_9, X_48, 9, 48, incident=True)
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_84 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C) - cos(A) - 1)', ID="X_84", classes=["center", "incident"])
            central_line(model, X_21, X_84, 21, 84, incident=True)
            return promote_point_to_top(model, X_3576)


        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_3576 on the given reference triangle."""
            model = create_model('X_3576 = INTERSECTION OF LINES X_1X_3 AND X_2X_515')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03576(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-03576.json"))
            write_center_svg(
                model_acute,
                here / "x-03576.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3576¶

X₃₅₇₆¶