← etc / Encyclopedia of Triangle Centers

X₁₃₅₃¶

REFLECTION OF X₅ IN X₆

X₁₃₅₃ is the reflection of X₅ in X₆.

X₁₃₅₃ (REFLECTION OF X₅ IN X₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1353 = REFLECTION OF X_5 IN X_6."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            midpoint,
            nine_point_center_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01353(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1353 = REFLECTION OF X_5 IN X_6 on reference triangle ABC."""
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_193 = eval_trilinear_point(model, A, B, C, '(csc(A))*(cot(B) + cot(C) - cot(A))', ID="X_193", classes=["center"])
            X_1353 = midpoint(model, X_3, X_193, ID="X_1353", classes=["selected", "target"], guide=False)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_5, X_6, 5, 6, incident=True)
            central_line(model, X_3, X_193, 3, 193, incident=True)
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_140 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B - C)', ID="X_140", classes=["center", "incident"])
            central_line(model, X_69, X_140, 69, 140, incident=True)
            return promote_point_to_top(model, X_1353)


        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_1353 on the given reference triangle."""
            model = create_model('X_1353 = REFLECTION OF X_5 IN X_6')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01353(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-01353.json"))
            write_center_svg(
                model_acute,
                here / "x-01353.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1353¶

X₁₃₅₃¶