IMO 1970 LL BEL11

Let ABCD and A′B′C′D′ be two squares in the same plane and

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IMO 1970 LL BEL11

Origin: BEL

Problem

Let ABCD and A′B′C′D′ be two squares in the same plane and oriented in the same direction. Let A′′, B′′, C′′, and D′′ be the midpoints of AA′, BB′, CC′, and DD′. Prove that A′′B′′C′′D′′ is also a square.