← etc / Encyclopedia of Triangle Centers

X₃₅₆₂¶

SS(sin A → cos A) OF X₁₆₂₁

X₃₅₆₂ = crosssum of X₆₄₇ and X₂₃₁₀

X₃₅₆₂ (SS(sin A → cos A) OF X₁₆₂₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3562 = SS(sin A → cos A) OF X_1621."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03562(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3562 = SS(sin A → cos A) OF X_1621 on reference triangle ABC."""
            X_3562 = eval_trilinear_point(model, A, B, C, '((cos(A))**(2) - cos(B)*cos(C) - cos(C)*cos(A) - cos(A)*cos(B))', ID="X_3562", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            central_line(model, X_1, X_21, 1, 21, incident=True)
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_77 = eval_trilinear_point(model, A, B, C, '1/(1 + sec(A))', ID="X_77", classes=["center", "incident"])
            central_line(model, X_40, X_77, 40, 77, incident=True)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_222 = eval_trilinear_point(model, A, B, C, 'cos(A)*tan(A/2)', ID="X_222", classes=["center", "incident"])
            central_line(model, X_20, X_222, 20, 222, incident=True)
            return promote_point_to_top(model, X_3562)


        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_3562 on the given reference triangle."""
            model = create_model('X_3562 = SS(sin A → cos A) OF X_1621')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03562(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-03562.json"))
            write_center_svg(
                model_acute,
                here / "x-03562.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3562¶

X₃₅₆₂¶