← etc / Encyclopedia of Triangle Centers

X₉₈₄¶

MIDPOINT OF X₈ AND X₁₉₂

X₉₈₄ is the midpoint of X₈ and X₁₉₂.

X₉₈₄ (MIDPOINT OF X₈ AND X₁₉₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_984 = MIDPOINT OF X_8 AND X_192."""

        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,
            incenter_of,
            midpoint,
            nagel_point_of,
            promote_point_to_top,
            spieker_center_of,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00984(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_984 = MIDPOINT OF X_8 AND X_192 on reference triangle ABC."""
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center"])
            X_192 = eval_trilinear_point(model, A, B, C, 'b*c*(c*a + a*b - b*c)', ID="X_192", classes=["center"])
            X_984 = midpoint(model, X_8, X_192, ID="X_984", classes=["selected", "target"], guide=False)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_1, X_6, 1, 6, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", 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_2, X_38, 2, 38, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            central_line(model, X_10, X_75, 10, 75, incident=True)
            return promote_point_to_top(model, X_984)


        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_984 on the given reference triangle."""
            model = create_model('X_984 = MIDPOINT OF X_8 AND X_192')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00984(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-00984.json"))
            write_center_svg(
                model_acute,
                here / "x-00984.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X984¶

X₉₈₄¶