Mathematical and Physical Journal
for High Schools
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Problem A. 748. (March 2019)

A. 748. The circles \(\displaystyle \Omega\) and \(\displaystyle \omega\) in its interior are fixed. The distinct points \(\displaystyle A\), \(\displaystyle B\), \(\displaystyle C\), \(\displaystyle D\), \(\displaystyle E\) move on \(\displaystyle \Omega\) in such a way that the line segments \(\displaystyle AB\), \(\displaystyle BC\), \(\displaystyle CD\) and \(\displaystyle DE\) are tangents to \(\displaystyle \omega\). The lines \(\displaystyle AB\) and \(\displaystyle CD\) meet at point \(\displaystyle P\), the lines \(\displaystyle BC\) and \(\displaystyle DE\) meet at \(\displaystyle Q\). Let \(\displaystyle R\) be the second intersection of the circles \(\displaystyle BCP\) and \(\displaystyle CDQ\), other than \(\displaystyle C\). Show that \(\displaystyle R\) moves either on a circle or on a line.

Proposed by: Carlos Yuzo Shine, Sao Paolo

(7 pont)

Deadline expired on April 10, 2019.


1 student sent a solution.
7 points:Schrettner Jakab.

Problems in Mathematics of KöMaL, March 2019