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X₁₆₅₆¶

INTERSECTION OF EULER LINE AND LINEX(17)X₁₈

Let A' be the reflection of X₃ in A, and define B' and C' cyclically. The triangle A'B'C' is homothetic to the medial triangle, and the center of homothety is X₁₆₅₆.

X₁₆₅₆ (INTERSECTION OF EULER LINE AND LINEX(17)X₁₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1656 = INTERSECTION OF EULER LINE AND LINEX(17)X_18."""

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


        def construct_x_01656(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1656 = INTERSECTION OF EULER LINE AND LINEX(17)X_18 on reference triangle ABC."""
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center"])
            X_632 = eval_trilinear_point(model, A, B, C, '7*cos(A) + 6*cos(B)*cos(C)', ID="X_632", classes=["center"])
            X_1656 = midpoint(model, X_5, X_632, ID="X_1656", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_17 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /6)', ID="X_17", classes=["center", "incident"])
            central_line(model, X_6, X_17, 6, 17, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_498 = eval_trilinear_point(model, A, B, C, '1 + 2*sin(B)*sin(C)', ID="X_498", classes=["center", "incident"])
            central_line(model, X_11, X_498, 11, 498, incident=True)
            return promote_point_to_top(model, X_1656)


        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_1656 on the given reference triangle."""
            model = create_model('X_1656 = INTERSECTION OF EULER LINE AND LINEX(17)X_18')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01656(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-01656.json"))
            write_center_svg(
                model_acute,
                here / "x-01656.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1656¶

X₁₆₅₆¶