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X₂₇₅¶

CEVAPOINT OF ORTHOCENTER AND SYMMEDIAN POINT

X₂₇₅ is the cevapoint of orthocenter and symmedian point.

X₂₇₅ (CEVAPOINT OF ORTHOCENTER AND SYMMEDIAN POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_275 = CEVAPOINT OF ORTHOCENTER AND SYMMEDIAN 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,
            centroid_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_00275(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_275 = CEVAPOINT OF ORTHOCENTER AND SYMMEDIAN POINT on reference triangle ABC."""
            X_216 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*cos(B - C)', ID="X_216", classes=["center"])
            X_275 = isogonal_conjugate(model, A, B, C, X_216, ID="X_275", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            central_line(model, X_4, X_54, 4, 54, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_95 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*sec(B - C)', ID="X_95", classes=["center", "incident"])
            central_line(model, X_2, X_95, 2, 95, incident=True)
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center", "incident"])
            central_line(model, X_51, X_107, 51, 107, incident=True)
            return promote_point_to_top(model, X_275)


        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_275 on the given reference triangle."""
            model = create_model('X_275 = CEVAPOINT OF ORTHOCENTER AND SYMMEDIAN POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00275(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-00275.json"))
            write_center_svg(
                model_acute,
                here / "x-00275.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X275¶

X₂₇₅¶