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X₁₂₁₇¶

CRETAN PERSPECTOR

Using barycentric coordinates, let P =\(p : q : r\) be a point not on a sideline of triangle ABC, and let P' be the isogonal conjugate of P. Let DEF and D'E'F' be the pedal triangles of P and P', respectively. Let

X = PD'∩P'D, Y = PE'∩P'E, Z = PF'∩P'F.

X₁₂₁₇ (CRETAN PERSPECTOR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1217 = CRETAN PERSPECTOR."""

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


        def construct_x_01217(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1217 = CRETAN PERSPECTOR on reference triangle ABC."""
            X_1181 = eval_trilinear_point(model, A, B, C, '((1 - cos(A)*sin(B)*sin(C))*cos(A))', ID="X_1181", classes=["center"])
            X_1217 = isogonal_conjugate(model, A, B, C, X_1181, ID="X_1217", classes=["selected", "target"])
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_97 = eval_trilinear_point(model, A, B, C, 'cot(A)*sec(B - C)', ID="X_97", classes=["center", "incident"])
            central_line(model, X_20, X_97, 20, 97, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_393 = eval_trilinear_point(model, A, B, C, 'b*c*(tan(A))**(2)', ID="X_393", classes=["center", "incident"])
            central_line(model, X_3, X_393, 3, 393, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_394 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A)', ID="X_394", classes=["center", "incident"])
            central_line(model, X_4, X_394, 4, 394, incident=True)
            return promote_point_to_top(model, X_1217)


        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_1217 on the given reference triangle."""
            model = create_model('X_1217 = CRETAN PERSPECTOR')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01217(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-01217.json"))
            write_center_svg(
                model_acute,
                here / "x-01217.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1217¶

X₁₂₁₇¶