Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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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.

### Statistics:

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

Problems in Mathematics of KöMaL, March 2019