Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem A. 419. (February 2007)

A. 419. The diagonals of a cyclic quadrilateral ABCD meet at X. The circles ABX and CDX meet again at Y. Take point Z such that triangles BZC and AYD are similar. Show that if BZCY is convex, then it has an inscribed circle.

(Russian competition problem)

(5 pont)

Deadline expired on March 19, 2007.


Statistics:

12 students sent a solution.
5 points:Dobribán Edgár, Fischer Richárd, Gyenizse Gergő, Kisfaludi-Bak Sándor, Korándi Dániel, Lovász László Miklós, Nagy 224 Csaba, Nagy 235 János, Nagy 314 Dániel, Sümegi Károly, Tomon István.
4 points:Hujter Bálint.

Problems in Mathematics of KöMaL, February 2007