← etc / Encyclopedia of Triangle Centers

X₃₃₀₅¶

INTERSECTION OF LINES X₁X_748 AND X₂X_7

X₃₃₀₅ = {X₂,X₉}-harmonic conjugate of X₆₃

X₃₃₀₅ (INTERSECTION OF LINES X₁X_748 AND X₂X_7) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3305 = INTERSECTION OF LINES X_1X_748 AND X_2X_7."""

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


        def construct_x_03305(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3305 = INTERSECTION OF LINES X_1X_748 AND X_2X_7 on reference triangle ABC."""
            X_3305 = eval_trilinear_point(model, A, B, C, '(2 + cos(A))*csc(A)', ID="X_3305", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_2, X_7, 2, 7, incident=True)
            X_78 = eval_trilinear_point(model, A, B, C, '1/(1 - sec(A))', ID="X_78", classes=["center", "incident"])
            X_405 = eval_trilinear_point(model, A, B, C, 'b*c*(a + b + c) + a*b*c*cos(A)', ID="X_405", classes=["center", "incident"])
            central_line(model, X_78, X_405, 78, 405, incident=True)
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_469 = point_from_barycentrics(model, A, B, C, 0.14569854, 0.21687036, 0.6374311, ID="X_469", classes=["center", "incident"])
            central_line(model, X_19, X_469, 19, 469, incident=True)
            return promote_point_to_top(model, X_3305)


        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_3305 on the given reference triangle."""
            model = create_model('X_3305 = INTERSECTION OF LINES X_1X_748 AND X_2X_7')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03305(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-03305.json"))
            write_center_svg(
                model_acute,
                here / "x-03305.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3305¶

X₃₃₀₅¶