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C. 861. In a partial Solar Eclipse, the apparent diameters of the Sun and the Moon were equal. In the time instant when the eclipse was at its maximum, the edge of the Moon's shadow passed through the centre of the Sun's face. What percentage of the Sun's face was eclipsed?

(5 points)

Deadline expired.


Google Translation (Sorry, the solution is published in Hungarian only.)

Megoldás: A terület két egybevágó körszelet területeként adódik:

T=2\cdot\left(\frac{r^2\pi}{3}-\frac{r^2\sin120^{\circ}}{2}\right)=r^2\left(\frac{2\pi}{3}-\frac{\sqrt3}{2}\right).

Így a kérdéses arány:

\frac{r^2\left(\frac{2\pi}{3}-\frac{\sqrt3}{2}\right)}{r^2\pi}=\frac{2}{3}-\frac{\sqrt3}{2\pi}\approx39,10\%.


Statistics on problem C. 861.
575 students sent a solution.
5 points:438 students.
4 points:60 students.
3 points:36 students.
2 points:14 students.
1 point:3 students.
0 point:16 students.
Unfair, not evaluated:8 solutions.


  • Problems in Mathematics of KöMaL, September 2006

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