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Please take a look at this PDF document, and see problem 17. Because it is written into georgian languages i will translate it in english. problem is following we have two circle with common center and AB and CD diameters which intersects each -other at right angles. there is given two condition

A)  area of large circle is 10 sm^2
B) area of  small circle is 2 sm^2

for find area of darkened part of big circle which one is correct

1)first condition is enough  and second not
2.second is enough and first not
3.both are enough  but not   seperately
4.it is enough  each seperately
5.both conditions are not enough,there is necessary  additional  statement

and one question more .for my opinion because these diameters intersect at right angles then area of each small sector is 1/4 of each big darkened sectors.am i right? thanks

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1 Answer 1

up vote 2 down vote accepted

If you translated the problem correctly, the small circle is entirely irrelevant; the area of the dark part of the big circle is just half the area of the big circle by symmetry, since the dark and white parts obviously correspond to each other and all of the big circle is either dark or white. If you reread the Georgian original, could it be that they mean only the outer dark parts of the big circle, the ones outside the small circle?

The answer to your other question is yes: The area of the inner circle is one quarter of the area of the outer annulus of the big circle, so the area of each of the four equal sectors is likewise one quarter of each of the sectors of the annulus.

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including these dark part which are in small circle –  dato datuashvili Jun 1 '11 at 10:46

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