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X₉₂¶

CEVAPOINT OF INCENTER AND CLAWSON POINT

Let L_A be the line through X₄ parallel to the internal bisector of angle A, and let

A' = BC∩L_A. Define B' and C' cyclically.

X₉₂ (CEVAPOINT OF INCENTER AND CLAWSON POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT."""

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


        def construct_x_00092(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT on reference triangle ABC."""
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center"])
            X_92 = isogonal_conjugate(model, A, B, C, X_48, ID="X_92", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            central_line(model, X_4, X_8, 4, 8, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_29 = eval_trilinear_point(model, A, B, C, '(sec(A))/(cos(B) + cos(C))', ID="X_29", classes=["center", "incident"])
            central_line(model, X_1, X_29, 1, 29, incident=True)
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_27 = eval_trilinear_point(model, A, B, C, '(sec(A))/(b + c)', ID="X_27", classes=["center", "incident"])
            central_line(model, X_19, X_27, 19, 27, incident=True)
            return promote_point_to_top(model, X_92)


        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_92 on the given reference triangle."""
            model = create_model('X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00092(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-00092.json"))
            write_center_svg(
                model_acute,
                here / "x-00092.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X92¶

X₉₂¶