1. 
The governor wants to build a new library for three cities X, Y, and Z. If the distance between each two cities is 16 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. 
I is the incenter of _{}ABC. If _{} = 104, _{} = 33, _{} = 121, and _{} = 16, find the area of _{}ABC.


3. 
In the figure, P is the incenter of _{}ABC, the radius of the inscribed circle is 4 cm, and the perimeter of _{}ABC is 39 cm. What is the area of _{}ABC?


4. 
ABC is an isosceles triangle. If _{} = _{} = 16, _{} = 10, D is the midpoint of side _{}, and G is the centroid of _{}ABC, find _{}.

