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The paper presents a problem that has all the components that make it usable as a research problem for both high school students and in training mathematics teachers at teacher training colleges and universities. The problem contains various geometric curves and shapes: squares, circles, sectors, segments, parabola. It can be developed in stages, asking additional questions that, on the one hand, increase the level of complexity, and on the other hand, reveal the beauty of mathematics.

Investigation on inscribed circles: one, two, three, four, infinitely many