Mathematical and Physical Journal
for High Schools
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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