Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 497. (February 2016)

K. 497. In a right-angled triangle \(\displaystyle ABC\), \(\displaystyle BC = 5\) and \(\displaystyle AB = 12\). \(\displaystyle M\) is the intersection of hypotenuse \(\displaystyle AC\) with the arc of radius \(\displaystyle AB\) centred at \(\displaystyle A\), and \(\displaystyle N\) is the intersection of hypotenuse \(\displaystyle AC\) with the arc \(\displaystyle BC\) centred at \(\displaystyle C\). Determine the distance between points \(\displaystyle M\) and \(\displaystyle N\).

(6 pont)

Deadline expired on March 10, 2016.


Statistics:

104 students sent a solution.
6 points:85 students.
5 points:4 students.
4 points:4 students.
3 points:7 students.
2 points:3 students.
Unfair, not evaluated:1 solution.

Problems in Mathematics of KöMaL, February 2016