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X₃₉₆¶

MIDPOINT OF X₁₃ AND X₁₅

X₃₉₆ is the center of the (equilateral) pedal triangle of X₁₅, as well as the circumcenter of the pedal triangle of X₁₃.

X₃₉₆ (MIDPOINT OF X₁₃ AND X₁₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_396 = MIDPOINT OF X_13 AND X_15."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nine_point_center_of,
            promote_point_to_top,
            reflection_in_point,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00396(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_396 = MIDPOINT OF X_13 AND X_15 on reference triangle ABC."""
            X_395 = eval_trilinear_point(model, A, B, C, 'cos(B - C) + 2*cos(A +  pi  /3)', ID="X_395", classes=["center"])
            X_230 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2)*(2*a**(2) - b**(2) - c**(2)) + (b**(2) - c**(2))**(2))', ID="X_230", classes=["center"])
            X_396 = reflection_in_point(model, X_395, X_230, ID="X_396", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_2, X_6, 2, 6, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_14 = eval_trilinear_point(model, A, B, C, 'csc(A -  pi  /3)', ID="X_14", classes=["center", "incident"])
            central_line(model, X_5, X_14, 5, 14, incident=True)
            X_13 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /3)', ID="X_13", classes=["center", "incident"])
            X_15 = eval_trilinear_point(model, A, B, C, 'sin(A +  pi  /3)', ID="X_15", classes=["center", "incident"])
            central_line(model, X_13, X_15, 13, 15, incident=True)
            return promote_point_to_top(model, X_396)


        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_396 on the given reference triangle."""
            model = create_model('X_396 = MIDPOINT OF X_13 AND X_15')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00396(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-00396.json"))
            write_center_svg(
                model_acute,
                here / "x-00396.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X396¶

X₃₉₆¶