← etc / Encyclopedia of Triangle Centers

X₁₂₃¶

X₁₀₈-OF-MEDIAL-TRIANGLE

X₁₂₃ (X₁₀₈-OF-MEDIAL-TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_123 = X_108-OF-MEDIAL-TRIANGLE."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            complement,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00123(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_123 = X_108-OF-MEDIAL-TRIANGLE on reference triangle ABC."""
            X_108 = eval_trilinear_point(model, A, B, C, 'a/(sec(B) - sec(C))', ID="X_108", classes=["center"])
            X_123 = complement(model, A, B, C, X_108, ID="X_123", classes=["selected", "target"])
            return promote_point_to_top(model, X_123)


        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_123 on the given reference triangle."""
            model = create_model('X_123 = X_108-OF-MEDIAL-TRIANGLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00123(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-00123.json"))
            write_center_svg(
                model_acute,
                here / "x-00123.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X123¶

X₁₂₃¶