Mathematical and Physical Journal
for High Schools
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Problem C. 821. (October 2005)

C. 821. A unit square ABCD is rotated about its vertex C through 90o. Determine the area swept out by the side AB.

(5 pont)

Deadline expired on November 15, 2005.


Sorry, the solution is available only in Hungarian. Google translation

Megoldás:

T=T_{AA'D}+T_{ABD}=\left((\sqrt2)^2\pi\cdot{1\over4}-1\right)+\left(1-1^2\cdot\pi\cdot{1\over4}\right)={\pi\over4}.


Statistics:

608 students sent a solution.
5 points:437 students.
4 points:44 students.
3 points:23 students.
2 points:9 students.
0 point:50 students.
Unfair, not evaluated:45 solutions.

Problems in Mathematics of KöMaL, October 2005