In the figure can the arc(PR) arc(RQ) be called similar?
2026-03-26 11:06:59.1774523219
Are the arcs on the same circle similar?
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No, two arcs of the same circle are similar only if they are congruent. Indeed, a (nondegenerate) arc of a circle has the property that there is a unique point (the center of the circle) which is equidistant from every point of the arc, with the two extreme points of the arc forming a certain angle at the center. This angle is preserved by any similarity. So if two arcs of circles are similar, they span the same angle at the center. If two arcs of the same circle span the same angle, they are congruent.
To provide some intuition, in your example if you tried to rescale the arc $PR$ so it had the same length as arc $RQ$, they would not be congruent because $PR$ would be an arc of a circle of smaller radius, and thus would be more sharply curved (further from being a straight line).