Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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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.

### 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.

Problems in Mathematics of KöMaL, February 2016