Mathematical and Physical Journal
for High Schools
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Problem A. 779. (May 2020)

A. 779. Two circles are given in the plane, \(\displaystyle \Omega\) and inside it \(\displaystyle \omega\). The center of \(\displaystyle \omega\) is \(\displaystyle I\). \(\displaystyle P\) is a point moving on \(\displaystyle \Omega\). The second intersection of the tangents from \(\displaystyle P\) to \(\displaystyle \omega\) and circle \(\displaystyle \Omega\) are \(\displaystyle Q\) and \(\displaystyle R\). The second intersection of circle \(\displaystyle IQR\) and lines \(\displaystyle PI\), \(\displaystyle PQ\) and \(\displaystyle PR\) are \(\displaystyle J\), \(\displaystyle S\) and \(\displaystyle T\), respectively. The reflection of point \(\displaystyle J\) across line \(\displaystyle ST\) is \(\displaystyle K\).

Prove that lines \(\displaystyle PK\) are concurrent.

(7 pont)

Deadline expired on June 10, 2020.


3 students sent a solution.
7 points:Bán-Szabó Áron, Beke Csongor, Weisz Máté.

Problems in Mathematics of KöMaL, May 2020