← etc / Encyclopedia of Triangle Centers

X₃₆₄₄¶

REFLECTION OF X₇₅ IN X₁₉₂

X₃₆₄₄ is the reflection of X₇₅ in X₁₉₂.

X₃₆₄₄ (REFLECTION OF X₇₅ IN X₁₉₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3644 = REFLECTION OF X_75 IN 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,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03644(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3644 = REFLECTION OF X_75 IN X_192 on reference triangle ABC."""
            X_3644 = eval_trilinear_point(model, A, B, C, '(b*c*(3/a - 2/b - 2/c))', ID="X_3644", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            central_line(model, X_2, X_37, 2, 37, incident=True)
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            X_1743 = eval_trilinear_point(model, A, B, C, '3*a - b - c', ID="X_1743", classes=["center", "incident"])
            central_line(model, X_190, X_1743, 190, 1743, incident=True)
            X_726 = eval_trilinear_point(model, A, B, C, '(a **(-3)*(b **(-1) + c **(-1)) - a **(-2)*(b **(-2) + c **(-2)))', ID="X_726", classes=["center", "incident"])
            X_3244 = eval_trilinear_point(model, A, B, C, 'b*c*(4*a - b - c)', ID="X_3244", classes=["center", "incident"])
            central_line(model, X_726, X_3244, 726, 3244, incident=True)
            return promote_point_to_top(model, X_3644)


        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_3644 on the given reference triangle."""
            model = create_model('X_3644 = REFLECTION OF X_75 IN X_192')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03644(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-03644.json"))
            write_center_svg(
                model_acute,
                here / "x-03644.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3644¶

X₃₆₄₄¶