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 \(\displaystyle PQR\sphericalangle =B_1 QC_1\sphericalangle\).


(5 pont)

Deadline expired on December 10, 2015.


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