Dan Ismailecu and Adam Vojdany, Class preserving dissections of convex quadrilaterals,
Forum Geometricorum, 9 (2009) 195--211.

Abstract: Given a convex quadrilateral Q having a certain property P, we are interested in finding a dissection of Q into a finite number of smaller convex quadrilaterals, each of which has property P as well. In particular, we prove that every cyclic, orthodiagonal, or circumscribed quadrilateral can be dissected into cyclic, orthodiagonal, or circumscribed quadrilaterals, respectively. The problem becomes much more interesting if we restrict our study to a particular type of partition we call grid dissection.

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