← etc / Encyclopedia of Triangle Centers

X₃₅₀₉¶

INTERSECTION OF LINES X₁X_32 AND X₂X_7

X₃₅₀₉ = isogonal cojugate of X₃₅₁₂

X₃₅₀₉ (INTERSECTION OF LINES X₁X_32 AND X₂X_7) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3509 = INTERSECTION OF LINES X_1X_32 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,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03509(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3509 = INTERSECTION OF LINES X_1X_32 AND X_2X_7 on reference triangle ABC."""
            X_3509 = eval_trilinear_point(model, A, B, C, '(a**(3) - b**(3) - c**(3) + a*b*c)', ID="X_3509", 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_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            central_line(model, X_1, X_32, 1, 32, incident=True)
            X_199 = eval_trilinear_point(model, A, B, C, '(a*(b**(4) + c**(4) - a**(4) + (b**(2) + c**(2) - a**(2))*(b*c + c*a + a*b)))', ID="X_199", classes=["center", "incident"])
            X_228 = eval_trilinear_point(model, A, B, C, '(sin(2*A))*(sin(B) + sin(C))', ID="X_228", classes=["center", "incident"])
            central_line(model, X_199, X_228, 199, 228, incident=True)
            return promote_point_to_top(model, X_3509)


        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_3509 on the given reference triangle."""
            model = create_model('X_3509 = INTERSECTION OF LINES X_1X_32 AND X_2X_7')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03509(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-03509.json"))
            write_center_svg(
                model_acute,
                here / "x-03509.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3509¶

X₃₅₀₉¶