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X₁₅₁₅¶

ORTHOJOIN OF X₄

X₁₅₁₅ = intersection of Simson line of X₁₀₇ (line X₁₃₃ X₁₅₁₅) and trilinear polar of X₁₀₇ (line X₄ X₆)

X₁₅₁₅ (ORTHOJOIN OF X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1515 = ORTHOJOIN OF 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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            intersect_lines,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01515(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1515 = ORTHOJOIN OF X_4 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center"])
            X_1294 = eval_barycentric_point(model, A, B, C, '1/(a**(6)*(b**(2) + c**(2)) - a**(4)*(3*b**(4) - 4*b**(2)*c**(2) + 3*c**(4)) + 3*a**(2)*(b**(2) - c**(2))**(2)*(b**(2) + c**(2)) - (b**(2) - c**(2))**(2)*(b**(4) + 4*b**(2)*c**(2) + c**(4)))', ID="X_1294", classes=["center"])
            central_line(model, X_4, X_6, 4, 6)
            central_line(model, X_30, X_1294, 30, 1294)
            X_1515 = intersect_lines(model, X_4, X_6, X_30, X_1294, ID="X_1515", classes=["selected", "target"])
            X_133 = eval_trilinear_point(model, A, B, C, '(sec(A))*((sin(2*B) - sin(2*C))**(2) + (sin(2*A))*(sin(2*B)) + (sin(2*A))*(sin(2*C)) - 2*(sin(2*B))*(sin(2*C)))*(2*sin(2*A) - sin(2*B) - sin(2*C))', ID="X_133", classes=["center", "incident"])
            X_1559 = point_from_barycentrics(model, A, B, C, 0.2024927, 0.25212191, 0.54538539, ID="X_1559", classes=["center", "incident"])
            central_line(model, X_133, X_1559, 133, 1559, incident=True)
            return promote_point_to_top(model, X_1515)


        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_1515 on the given reference triangle."""
            model = create_model('X_1515 = ORTHOJOIN OF X_4')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01515(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-01515.json"))
            write_center_svg(
                model_acute,
                here / "x-01515.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1515¶

X₁₅₁₅¶