MathDB

5

Part of 2016 China National Olympiad

Problems(1)

Existence of square with properties

Source: China Mathematical Olympiad 2016 Q5

12/17/2015
Let ABCDABCD be a convex quadrilateral. Show that there exists a square A′B′C′D′A'B'C'D' (Vertices maybe ordered clockwise or counter-clockwise) such that A≠A′,B≠B′,C≠C′,D≠D′A \not = A', B \not = B', C \not = C', D \not = D' and AA′,BB′,CC′,DD′AA',BB',CC',DD' are all concurrent.
geometry