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X₁₄₈₇¶

NAPOLEON CEVAPOINT

Let N denote the nine-point center, X₅. Let N_A = N-of-triangle NBC, and define N_B and N_C cyclically. Triangle N_AN_BN_C is perspective to ABC, and X₁₄₈₇ is the perspector. X₁₄₈₇ is the cevapoint of the Napoleon points, X₁₇ and X₁₈. (Coordinates found by Paul Yiu.)

X₁₄₈₇ (NAPOLEON CEVAPOINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1487 = NAPOLEON CEVAPOINT."""

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


        def construct_x_01487(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1487 = NAPOLEON CEVAPOINT on reference triangle ABC."""
            X_1487 = eval_trilinear_point(model, A, B, C, '((csc(A))/((3 - cot(B)*cot(C))*(3 - (cot(A))**(2))))', ID="X_1487", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_252 = eval_trilinear_point(model, A, B, C, '(sec(B - C)/(1 - 2*cos(2*A)))', ID="X_252", classes=["center", "incident"])
            central_line(model, X_4, X_252, 4, 252, incident=True)
            X_140 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B - C)', ID="X_140", classes=["center", "incident"])
            X_930 = eval_barycentric_point(model, A, B, C, '1/((b**(2) - c**(2))*(a**(4) + b**(4) + c**(4) - 2*a**(2)*b**(2) - 2*a**(2)*c**(2) - b**(2)*c**(2)))', ID="X_930", classes=["center", "incident"])
            central_line(model, X_140, X_930, 140, 930, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_1173 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(4) - 3*a**(2)*(b**(2) + c**(2)) + (b**(2) - c**(2))**(2))', ID="X_1173", classes=["center", "incident"])
            central_line(model, X_5, X_1173, 5, 1173, incident=True)
            return promote_point_to_top(model, X_1487)


        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_1487 on the given reference triangle."""
            model = create_model('X_1487 = NAPOLEON CEVAPOINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01487(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-01487.json"))
            write_center_svg(
                model_acute,
                here / "x-01487.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1487¶

X₁₄₈₇¶