1. 
If O is the circumcenter of _{}ABC and m_{}C = 39, find m_{}AOB.


2. 
The perpendicular bisectors of _{}ABC meet at point G. If _{} = 12, _{} = 6, and _{} = 3, find _{}.


3. 
The governor wants to build a new library for three cities X, Y, and Z. If the distance between each two cities is 12 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? 

4. 
The angle bisectors of _{}ABC meet at point I, _{}:_{}:_{} = 2:6:6, and the area of _{}ABC is 84. What is the area of _{}BCI?


5. 
Medians _{}, _{}, and _{} of _{}ABC meet at G, _{} intersects _{} at H, and _{} = 18. Find _{}.


6. 
In the figure, P is the incenter of _{}ABC, the radius of the inscribed circle is 4 cm, and the perimeter of _{}ABC is 41 cm. What is the area of _{}ABC?

