Mathematical and Physical Journal
for High Schools
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Problem K. 89. (September 2006)

K. 89. Find the radius of the three congruent circles in the Figure, given that the side of the equilateral triangle is 12 cm.

(6 pont)

Deadline expired on October 10, 2006.


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

Megoldás: A szabályos háromszög oldala 12 cm, tehát magassága 6\sqrt3 cm. A kis kör sugarát nevezzük el r-nek, ekkor az ábra alapján a háromszög magassága r + \sqrt3r+2r = 3r+\sqrt3r. Tehát 3r+\sqrt3r=6\sqrt3. Ebből: r=\frac{6\sqrt3}{3+\sqrt3} cm, egyszerűbb alakban 3\sqrt3-3\approx2,2 cm.


Statistics:

230 students sent a solution.
6 points:68 students.
5 points:45 students.
4 points:30 students.
3 points:13 students.
2 points:6 students.
1 point:6 students.
0 point:50 students.
Unfair, not evaluated:12 solutions.

Problems in Mathematics of KöMaL, September 2006