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X₃₆₅₁¶

KS(1st CIRCUMPERP TRIANGLE)

For a construction of X₃₆₅₁ as the orthocenter of a certain triangle, see: Antreas Hatzipolakis and César Lozada, Hyacinthos 29288.

X₃₆₅₁ (KS(1st CIRCUMPERP TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3651 = KS(1st CIRCUMPERP TRIANGLE)."""

        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,
            midpoint,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03651(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3651 = KS(1st CIRCUMPERP TRIANGLE) on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_2475 = eval_trilinear_point(model, A, B, C, '(b*c*(a**(4) + a**(2)*b*c + a*b*c*(b + c) - (b**(2) - c**(2))**(2)))', ID="X_2475", classes=["center"])
            X_3651 = midpoint(model, X_2, X_2475, ID="X_3651", classes=["selected", "target"], guide=False)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_35 = eval_trilinear_point(model, A, B, C, '1 + 2*cos(A)', ID="X_35", classes=["center", "incident"])
            X_79 = eval_trilinear_point(model, A, B, C, '1/(1 + 2*cos(A))', ID="X_79", classes=["center", "incident"])
            central_line(model, X_35, X_79, 35, 79, incident=True)
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_72, X_74, 72, 74, incident=True)
            return promote_point_to_top(model, X_3651)


        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_3651 on the given reference triangle."""
            model = create_model('X_3651 = KS(1st CIRCUMPERP TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03651(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-03651.json"))
            write_center_svg(
                model_acute,
                here / "x-03651.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3651¶

X₃₆₅₁¶