← etc / Encyclopedia of Triangle Centers

X₃₅₇₄¶

INTERSECTION OF LINES X₄X_54 AND X₅X_51

X₃₅₇₄ = midpoint of X₄ and X₅₄

X₃₅₇₄ (INTERSECTION OF LINES X₄X_54 AND X₅X_51) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3574 = INTERSECTION OF LINES X_4X_54 AND X_5X_51."""

        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,
            midpoint,
            nine_point_center_of,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03574(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3574 = INTERSECTION OF LINES X_4X_54 AND X_5X_51 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center"])
            X_3574 = midpoint(model, X_4, X_54, ID="X_3574", classes=["selected", "target"], guide=False)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            central_line(model, X_5, X_51, 5, 51, incident=True)
            central_line(model, X_4, X_54, 4, 54, incident=True)
            X_113 = eval_trilinear_point(model, A, B, C, 'sin(B)*sin(C)*((sin(C))/(cos(C) - 2*cos(A)*cos(B)) + (sin(B))/(cos(B) - 2*cos(A)*cos(C)))', ID="X_113", classes=["center", "incident"])
            X_137 = point_from_barycentrics(model, A, B, C, 0.1354431, 0.64976082, 0.21479608, ID="X_137", classes=["center", "incident"])
            central_line(model, X_113, X_137, 113, 137, incident=True)
            return promote_point_to_top(model, X_3574)


        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_3574 on the given reference triangle."""
            model = create_model('X_3574 = INTERSECTION OF LINES X_4X_54 AND X_5X_51')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03574(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-03574.json"))
            write_center_svg(
                model_acute,
                here / "x-03574.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3574¶

X₃₅₇₄¶