Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4721. (May 2015)

B. 4721. A circle $\displaystyle k$ touches the legs $\displaystyle AB$ and $\displaystyle AC$ of an isosceles triangle $\displaystyle ABC$, and intersects the base $\displaystyle BC$ at $\displaystyle K$ and $\displaystyle L$. Line segment $\displaystyle AK$ intersects the circle $\displaystyle k$ again at point $\displaystyle M$. The reflections of point $\displaystyle K$ in $\displaystyle B$ and in $\displaystyle C$ are $\displaystyle P$ and $\displaystyle Q$, respectively. Prove that $\displaystyle k$ is tangent to the circumscribed circle of triangle $\displaystyle PMQ$.

(6 pont)

Deadline expired on June 10, 2015.

### Statistics:

 16 students sent a solution. 6 points: Andó Angelika, Cseh Kristóf, Csépai András, Fekete Panna, Glasznova Maja, Nagy-György Pál, Németh 123 Balázs, Schrettner Bálint, Schwarcz Tamás, Szebellédi Márton, Török Tímea, Williams Kada. 5 points: Andi Gabriel Brojbeanu. 4 points: 1 student. 3 points: 1 student. 2 points: 1 student.

Problems in Mathematics of KöMaL, May 2015