Mathematical and Physical Journal
for High Schools
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# Problem B. 4746. (November 2015)

B. 4746. The inscribed circle of triangle $\displaystyle ABC$ touches sides $\displaystyle BC$, $\displaystyle AC$ and $\displaystyle AB$ at points $\displaystyle A_1$, $\displaystyle B_1$ and $\displaystyle C_1$, respectively. The other intersection of line segment $\displaystyle AA_1$ with the inscribed circle is $\displaystyle Q$. The line through point $\displaystyle A$ parallel to $\displaystyle BC$ intersects the lines $\displaystyle A_1 C_1$ and $\displaystyle A_1 B_1$ at points $\displaystyle P$ and $\displaystyle R$. Prove that $\displaystyle PQR\sphericalangle =B_1 QC_1\sphericalangle$.

(Kvant)

(5 pont)

Deadline expired on December 10, 2015.

### Statistics:

 77 students sent a solution. 5 points: 62 students. 4 points: 5 students. 3 points: 4 students. 2 points: 3 students. 1 point: 2 students. Unfair, not evaluated: 1 solution.

Problems in Mathematics of KöMaL, November 2015