Problem K. 195.

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K. 195. The isosceles triangle ABC has a right angle at A; the length of its legs is AB=AC=4 cm. The circles with centers at B and C of radius 4 cm intersect the hypotenuse at D and E, respectively. What is the area of the shaded domain? (See the Figure.)

(6 points)

Deadline expired.

Sorry, the solution is published in Hungarian only.

Megoldás. A satírozott területet jelölje T. Ezen kívül keletkezik még két egybevágó alakzat, ezek területe felírható: $t=t_{\triangle}-\frac{45}{360}\cdot4^2\pi=\frac{4\cdot4}{2}-2\pi=8-2\pi$ .

Így a terület:

$T=t_{\triangle}-2t=8-2(8-2\pi)=4\pi-8\approx 4,5664.$

Statistics on problem K. 195.

170 students sent a solution.

6 points: 55 students.

5 points: 50 students.

4 points: 30 students.

3 points: 12 students.

2 points: 7 students.

1 point: 1 student.

0 point: 8 students.

Unfair, not evaluated: 7 solutions.

Problems in Mathematics of KöMaL, January 2009

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