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X₁₃₁¶

INTERSECTION OF LINES X₃X_125 AND X₄X_135

X₁₃₁ = X₁₀₂-of-orthic triangle if ABC is acute.

X₁₃₁ (INTERSECTION OF LINES X₃X_125 AND X₄X_135) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_131 = INTERSECTION OF LINES X_3X_125 AND X_4X_135."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            intersect_lines,
            nine_point_center_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00131(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_131 = INTERSECTION OF LINES X_3X_125 AND X_4X_135 on reference triangle ABC."""
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_135 = eval_trilinear_point(model, A, B, C, '(sec(A))*((sin(2*B))/(sec(2*C) - sec(2*A)) + (sin(2*C))/(sec(2*A) - sec(2*B)))', ID="X_135", classes=["center"])
            central_line(model, X_3, X_125, 3, 125)
            central_line(model, X_4, X_135, 4, 135)
            X_131 = intersect_lines(model, X_3, X_125, X_4, X_135, ID="X_131", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_136 = eval_barycentric_point(model, A, B, C, '(b**(2) - c**(2))**(2)*(a**(4) + b**(4) + c**(4) - 2*a**(2)*b**(2) - 2*a**(2)*c**(2))/(a**(2) - b**(2) - c**(2))', ID="X_136", classes=["center", "incident"])
            central_line(model, X_5, X_136, 5, 136, incident=True)
            return promote_point_to_top(model, X_131)


        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_131 on the given reference triangle."""
            model = create_model('X_131 = INTERSECTION OF LINES X_3X_125 AND X_4X_135')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00131(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-00131.json"))
            write_center_svg(
                model_acute,
                here / "x-00131.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X131¶

X₁₃₁¶