Mathematical and Physical Journal
for High Schools
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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.


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.

Problems in Mathematics of KöMaL, February 2016