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X₁₅₆₅¶

ORTHOJOIN OF X₆₅₇

X₁₅₆₅ = midpoint of X₁₅₀ and X₆₆₄

X₁₅₆₅ (ORTHOJOIN OF X₆₅₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1565 = ORTHOJOIN OF X_657."""

        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,
            gergonne_point_of,
            midpoint,
            nine_point_center_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01565(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1565 = ORTHOJOIN OF X_657 on reference triangle ABC."""
            X_150 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(4) + c**(4) - a**(4) + a*(b*c**(2) +c*b**(2) - b**(3) - c**(3)) - b*c*(a**(2) + b**(2) + c**(2)) + (b + c)*a**(3)))', ID="X_150", classes=["center"])
            X_664 = eval_trilinear_point(model, A, B, C, '1/(a*(b - c)*(b + c - a))', ID="X_664", classes=["center"])
            X_1565 = midpoint(model, X_150, X_664, ID="X_1565", classes=["selected", "target"], guide=False)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_85 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c - a)', ID="X_85", classes=["center", "incident"])
            central_line(model, X_5, X_85, 5, 85, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            central_line(model, X_7, X_104, 7, 104, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_279 = eval_trilinear_point(model, A, B, C, 'csc(A)*(tan(A/2))**(2)', ID="X_279", classes=["center", "incident"])
            central_line(model, X_4, X_279, 4, 279, incident=True)
            return promote_point_to_top(model, X_1565)


        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_1565 on the given reference triangle."""
            model = create_model('X_1565 = ORTHOJOIN OF X_657')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01565(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-01565.json"))
            write_center_svg(
                model_acute,
                here / "x-01565.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1565¶

X₁₅₆₅¶