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I am wondering if it is possible to map a (convex) quadrilateral to a cyclic quadrilateral by a homothety? Or is the property of being a cyclic quadrilateral preserved by a homothehty?

I would be very happy, if someone can give an example for illustrating his answer.

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A homothety is an angle preserving transformation. As a quadrilateral is cyclic iff opposite angles are supplementary, homothety preserves the class of cyclic quadrilaterals.

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