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.

Statistics:

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

Problems in Mathematics of KöMaL, May 2020