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