← etc / Encyclopedia of Triangle Centers

X₇₄₈¶

INTERSECTION OF LINES X₂X_31 AND X₉X_38

X₇₄₈ (INTERSECTION OF LINES X₂X_31 AND X₉X_38) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_748 = INTERSECTION OF LINES X_2X_31 AND X_9X_38."""

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


        def construct_x_00748(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_748 = INTERSECTION OF LINES X_2X_31 AND X_9X_38 on reference triangle ABC."""
            X_748 = eval_trilinear_point(model, A, B, C, 'a**(2) - 2*b*c', ID="X_748", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            central_line(model, X_2, X_31, 2, 31, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_38 = eval_trilinear_point(model, A, B, C, 'b**(2) + c**(2)', ID="X_38", classes=["center", "incident"])
            central_line(model, X_9, X_38, 9, 38, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_212 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 + cos(A))', ID="X_212", classes=["center", "incident"])
            central_line(model, X_11, X_212, 11, 212, incident=True)
            return promote_point_to_top(model, X_748)


        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_748 on the given reference triangle."""
            model = create_model('X_748 = INTERSECTION OF LINES X_2X_31 AND X_9X_38')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00748(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-00748.json"))
            write_center_svg(
                model_acute,
                here / "x-00748.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X748¶

X₇₄₈¶