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A square or an equilateral triangle for example when a circle is inscribed within it.
Draw a circle using a compass. Then, without changing the compass setting, place its point on the circumference of the circle, at any point A, and draw two arcs to intersect the circumference at B and C. Move the compass to B and draw another arc to intersect the circumference at D; and then from C to E. ADE will be an inscribed equilateral triangle.
That is the definition of the incenter; it is the center of the inscribed circle.
The answer is circumcenter