1. 
The governor wants to build a new library for three cities X, Y, and Z. If the distance between each two cities is 20 kilometers, and the location of the new library will be in equidistance to all three cities, what is the distance between the new library and city X? 

2. 
If O is the circumcenter of _{}ABC and m_{}C = 38, find m_{}AOB.


3. 
ABC is an isosceles triangle. If _{} = _{} = 14, _{} = 12, D is the midpoint of side _{}, and G is the centroid of _{}ABC, find _{}.


4. 
In the figure, P is the incenter of _{}ABC, the radius of the inscribed circle is 6 cm, and the perimeter of _{}ABC is 42 cm. What is the area of _{}ABC?


5. 
The angle bisectors of _{}ABC meet at point I, _{}:_{}:_{} = 2:5:5, and the area of _{}ABC is 48. What is the area of _{}BCI? 

6. 
_{} and _{} are medians of _{}ABC. If _{} = 3_{}, what is the ratio of areas of _{}GBH and _{}ABC?

