← etc / Encyclopedia of Triangle Centers

X₁₁₇¶

MIDPOINT OF X₄ AND X₁₀₉

X₁₁₇ is the midpoint of X₄ and X₁₀₉.

X₁₁₇ (MIDPOINT OF X₄ AND X₁₀₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_117 = MIDPOINT OF X_4 AND X_109."""

        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,
            intersect_lines,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00117(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_117 = MIDPOINT OF X_4 AND X_109 on reference triangle ABC."""
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_102 = eval_trilinear_point(model, A, B, C, '1/(sin(B)*(sec(A) - sec(B)) + sin(C)*(sec(A) - sec(C)))', ID="X_102", classes=["center"])
            central_line(model, X_11, X_65, 11, 65)
            central_line(model, X_2, X_102, 2, 102)
            X_117 = intersect_lines(model, X_11, X_65, X_2, X_102, ID="X_117", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            central_line(model, X_4, X_109, 4, 109, incident=True)
            return promote_point_to_top(model, X_117)


        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_117 on the given reference triangle."""
            model = create_model('X_117 = MIDPOINT OF X_4 AND X_109')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00117(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-00117.json"))
            write_center_svg(
                model_acute,
                here / "x-00117.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X117¶

X₁₁₇¶