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X₃₀₉₁¶

INTERSECTION OF LINES X₂X_3 AND X₁₁X_153

X₃₀₉₁ = midpoint of X₄ and X₆₃₁

X₃₀₉₁ (INTERSECTION OF LINES X₂X_3 AND X₁₁X_153) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3091 = INTERSECTION OF LINES X_2X_3 AND X_11X_153."""

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


        def construct_x_03091(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3091 = INTERSECTION OF LINES X_2X_3 AND X_11X_153 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_631 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B)*cos(C)', ID="X_631", classes=["center"])
            X_3091 = midpoint(model, X_4, X_631, ID="X_3091", classes=["selected", "target"], guide=False)
            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_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_153 = eval_barycentric_point(model, A, B, C, 'a**(7) - a**(6)*(b + c) - a**(5)*(b**(2) - 7*b*c + c**(2)) + a**(4)*(b + c)*(b**(2) - 6*b*c + c**(2)) - a**(3)*(b**(4) + 2*b**(3)*c - 10*b**(2)*c**(2) + 2*b*c**(3) + c**(4)) + a**(2)*(b - c)**(2)*(b + c)*(b**(2) + 6*b*c + c**(2)) + a*(b**(2) - c**(2))**(2)*(b**(2) - 5*b*c + c**(2)) - (b - c)**(4)*(b + c)**(3)', ID="X_153", classes=["center", "incident"])
            central_line(model, X_11, X_153, 11, 153, incident=True)
            X_114 = eval_trilinear_point(model, A, B, C, 'b*c*(b*sec(B +  omega  ) + c*sec(C +  omega  ))', ID="X_114", classes=["center", "incident"])
            X_148 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) - (b**(2) - c**(2))**(2) + b**(2)*c**(2) - a**(2)*b**(2) - a**(2)*c**(2))', ID="X_148", classes=["center", "incident"])
            central_line(model, X_114, X_148, 114, 148, incident=True)
            return promote_point_to_top(model, X_3091)


        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_3091 on the given reference triangle."""
            model = create_model('X_3091 = INTERSECTION OF LINES X_2X_3 AND X_11X_153')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03091(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-03091.json"))
            write_center_svg(
                model_acute,
                here / "x-03091.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3091¶

X₃₀₉₁¶