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IGO 2016 Advanced/5

Unread postPosted: Tue Jan 10, 2017 4:33 pm
by Thamim Zahin
5. Do there exist six points $X_1,X_2, Y_1,Y_2,Z_1,Z_2$ in the plane such that all of the triangles $X_iY_jZ_k$ are similar for $1 \le i, j, k \le 2$?