Place as many points as possible on a plane so that any three points do not lie on the same line and are vertices of an isosceles triangle.

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The maximum number of points is six: a regular pentagon and its center (see figure).

![](https://cdn.mathpix.com/cropped/2024_05_06_39480ed8b0d60d88e837g-35.jpg?height=323&width=332&top_left_y=876&top_left_x=860)