# Circle Geometry Circle Solutions 1 for GMAT

## 1

Let us name the radius of C centered small circle as X. BC is the hypotenus of the right triangle therefore hypotenus will be x√2. Same way for the O centered circle BO is the hypotenus and thelength is 5√2. We can create our equation from these information as following

5√2 = 5 + x + x√2

When solve the equation for x. you will find the x.

**Correct choice is A**

## 2.

If draw a line from center 0 passing through center C. It would be radius of big circle. It is goign to be equal to** r*√2+r=5**

If we resolved the equation we will get choice A.

**Correct choice is A**

## 3.

when we draw those red lines. We can discover that AOF and AOD are congruent triangles. If r is the radius of the 0 centered circle then AF is 5-r. Since AOF is congruent to AOD triangle. AD is 5-r too. Same way OEC and ODC are congruent. CD is 12-r.

Since AC is 13 due to being hypotenus of the triangle. We can reach to following equation.

5-r+12-r = 13 when solve this equation we can find r = 2

**Correct choice is D**

## 4.

If we draw a line from A to H, it will be the height of the equilateral triangle its length is 5√3

5√3 = 5 + r_{2 }+ r_{2√3}

If we resolve this equation for r_{2 }we get choice E

**Correct choice is E**

## 5

If we draw a diagonal line between B and D point, we would split the area into half. Now each side of that area is actually equal to a quarter of full circle minus ABD triangle area. Therefore;

Shaded area equals to 2*(0.25*Π*10^{2}-10*10*0.5) = 50Π - 100

**Correct choice is C**

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