How many center of rotation are in the square, rectangle,Rhombus circles and a semi circle

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Solution

ShapeCentreofRotationOrderofRotationAngleofRotationSquareIntersectingpointofdiagonals490∘RectangleIntersectingpointofdiagonals2180∘RhombusIntersectingpointofdiagonals2180∘EquilateraltriangleIntersectingpointofmedians3120∘RegularhexagonIntersectingpointofdiagonals660∘CircleCentreInfiniteAteverypointSemi−circleMid−pointofdiameter1360∘

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\begin{matrix} S h a p e & C e n t r e o f R o t a t i o n & O r d e r o f R o t a t i o n & A n g l e o f R o t a t i o n S q u a r e R e c t a n g l e R h o m b u s E q u i l a t e r a l t r i a n g l e R e g u l a r h e x a g o n C i r c l e S e m i - c i r c l e \end{matrix}

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Prove that :

(i) the parallelogram, inscribed in a circle, is a rectangle.

(ii) the rhombus, inscribed in a circle, is a square.

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