Problem C. 1340. (February 2016)
C. 1340. Points \(\displaystyle P\), \(\displaystyle Q\), \(\displaystyle R\), \(\displaystyle S\) lie on sides \(\displaystyle AB\), \(\displaystyle BC\), \(\displaystyle CD\), \(\displaystyle DA\) of a rectangle \(\displaystyle ABCD\), respectively. Line segments \(\displaystyle PR\) and \(\displaystyle QS\) are perpendicular. Prove that the midpoints of line segments \(\displaystyle SP\), \(\displaystyle PQ\), \(\displaystyle QR\) and \(\displaystyle RS\) form a rectangle, which is similar to \(\displaystyle ABCD\).
(5 pont)
Deadline expired on March 10, 2016.
Statistics:
124 students sent a solution.  
5 points:  88 students. 
4 points:  8 students. 
3 points:  20 students. 
2 points:  7 students. 
0 point:  1 student. 
