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X₃₈₁¶

MIDPOINT OF X₂ AND X₄

X₃₈₁ is the point QA-P14 (Centroid of the Morley Triangle) of quadrangle ABCX₂ (see http://www.chrisvantienhoven.nl/quadrangle-objects/15-mathematics/quadrangle-objects/artikelen-qa/42-qa-p14.html)

X₃₈₁ (MIDPOINT OF X₂ AND X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_381 = MIDPOINT OF X_2 AND X_4."""

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


        def construct_x_00381(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_381 = MIDPOINT OF X_2 AND X_4 on reference triangle ABC."""
            X_381 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A)', ID="X_381", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_13 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /3)', ID="X_13", classes=["center", "incident"])
            central_line(model, X_6, X_13, 6, 13, incident=True)
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            X_156 = eval_barycentric_point(model, A, B, C, 'a**(2)*(a**(8) - 3*a**(6)*(b**(2) + c**(2)) + a**(4)*(3*b**(4) + 2*b**(2)*c**(2) + 3*c**(4)) - a**(2)*(b**(6) + c**(6)) + b**(2)*c**(2)*(b**(2) - c**(2))**(2))', ID="X_156", classes=["center", "incident"])
            central_line(model, X_54, X_156, 54, 156, incident=True)
            return promote_point_to_top(model, X_381)


        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_381 on the given reference triangle."""
            model = create_model('X_381 = MIDPOINT OF X_2 AND X_4')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00381(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-00381.json"))
            write_center_svg(
                model_acute,
                here / "x-00381.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X381¶

X₃₈₁¶