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 solutions.
Problems in Mathematics of KöMaL, November 2015