Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# Problem K. 268. (November 2010)

K. 268. How long is the radius of the circle in which a chord of length 6 units is twice as far away from the centre as a chord of length 12 units?

(6 pont)

Deadline expired on December 10, 2010.

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

Megoldás. A húrok szimmetriatengelye és a végpontokba a kör középpontjából húzott szakaszok derékszögű háromszögeket határoznak meg (ld. ábra), melyekben Pithagorasz tételét felírva: $\displaystyle 4d^2 + 9 =r^2 = d^2 +36$, ahonnan $\displaystyle d^2=9$, azaz ($\displaystyle d>0$ miatt) $\displaystyle d=3$. Ezért a kör sugara $\displaystyle \sqrt 5$, a két húr távolsága pedig $\displaystyle 3\sqrt 5$.

### Statistics:

 204 students sent a solution. 6 points: 77 students. 5 points: 45 students. 4 points: 13 students. 3 points: 32 students. 2 points: 15 students. 1 point: 1 student. 0 point: 12 students. Unfair, not evaluated: 9 solutionss.

Problems in Mathematics of KöMaL, November 2010