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X₃₆₆₀¶

MIDPOINT OF {X₃₅₁₃, X₃₅₁₄}

X₃₆₆₀ is the midpoint of {X₃₅₁₃, X₃₅₁₄}.

X₃₆₆₀ (MIDPOINT OF {X₃₅₁₃, X₃₅₁₄}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3660 = MIDPOINT OF {X_3513, X_3514}."""

        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_barycentric_point,
            eval_trilinear_point,
            incenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03660(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3660 = MIDPOINT OF {X_3513, X_3514} on reference triangle ABC."""
            X_3660 = eval_barycentric_point(model, A, B, C, '(a*(a - b + c)*(a + b - c)*(b**(3) + c**(3) + a**(2)*b + a**(2)*c - 2*a*b**(2) - 2*a*c**(2) + 2*a*b*c - b**(2)*c - b*c**(2)))', ID="X_3660", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            central_line(model, X_1, X_3, 1, 3, incident=True)
            X_222 = eval_trilinear_point(model, A, B, C, 'cos(A)*tan(A/2)', ID="X_222", classes=["center", "incident"])
            X_614 = eval_trilinear_point(model, A, B, C, 'a**(2) + b**(2) + c**(2) - 2*b*c', ID="X_614", classes=["center", "incident"])
            central_line(model, X_222, X_614, 222, 614, incident=True)
            X_108 = eval_trilinear_point(model, A, B, C, 'a/(sec(B) - sec(C))', ID="X_108", classes=["center", "incident"])
            X_840 = point_from_barycentrics(model, A, B, C, 0.66666667, -0.32, 0.65333333, ID="X_840", classes=["center", "incident"])
            central_line(model, X_108, X_840, 108, 840, incident=True)
            return promote_point_to_top(model, X_3660)


        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_3660 on the given reference triangle."""
            model = create_model('X_3660 = MIDPOINT OF {X_3513, X_3514}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03660(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-03660.json"))
            write_center_svg(
                model_acute,
                here / "x-03660.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3660¶

X₃₆₆₀¶