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