← etc / Encyclopedia of Triangle Centers

X₁₅₃₁¶

ORTHOJOIN OF X₃₂

X₁₅₃₁ = orthopole of de Longchamps line

X₁₅₃₁ (ORTHOJOIN OF X₃₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1531 = ORTHOJOIN OF X_32."""

        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_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01531(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1531 = ORTHOJOIN OF X_32 on reference triangle ABC."""
            X_1531 = eval_trilinear_point(model, A, B, C, '(2*a**(4) - a**(2)*(b**(2) + c**(2)) - b**(4) - c**(4) + 2*b**(2)*c**(2))*(a**(5) - a*(b**(2) - c**(2))**(2) - 4*b*c*(b**(3)*cos(B) + c**(3)*cos(C)))', ID="X_1531", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_4, X_69, 4, 69, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_113 = eval_trilinear_point(model, A, B, C, 'sin(B)*sin(C)*((sin(C))/(cos(C) - 2*cos(A)*cos(B)) + (sin(B))/(cos(B) - 2*cos(A)*cos(C)))', ID="X_113", classes=["center", "incident"])
            central_line(model, X_30, X_113, 30, 113, incident=True)
            X_382 = eval_trilinear_point(model, A, B, C, 'cos(A) - 4*cos(B)*cos(C)', ID="X_382", classes=["center", "incident"])
            X_1092 = eval_trilinear_point(model, A, B, C, '((cos(A))**(3))', ID="X_1092", classes=["center", "incident"])
            central_line(model, X_382, X_1092, 382, 1092, incident=True)
            return promote_point_to_top(model, X_1531)


        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_1531 on the given reference triangle."""
            model = create_model('X_1531 = ORTHOJOIN OF X_32')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01531(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-01531.json"))
            write_center_svg(
                model_acute,
                here / "x-01531.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1531¶

X₁₅₃₁¶