Problem:
A triangle has sides $\frac{11}{2}, 7, \frac{17}{2}$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, and symmedian point of the triangle.
Answer:
Orthocenter: $\left\{\frac{91}{17},\frac{1391}{68 \sqrt{30}}\right\}$ 
NinePointCenter: $\left\{\frac{653}{136},\frac{3071}{272 \sqrt{30}}\right\}$ 
Circumcenter: $\left\{\frac{17}{4},\frac{17}{8 \sqrt{30}}\right\}$ 
SymmedianPoint: $\left\{\frac{1071}{202},\frac{119 \sqrt{\frac{10}{3}}}{101}\right\}$ 
Incenter: $\left\{5,\sqrt{\frac{10}{3}}\right\}$ 
Centroid: $\left\{\frac{157}{34},\frac{14 \sqrt{\frac{10}{3}}}{17}\right\}$
{'source': 'AMPS', 'file': 'amps/mathematica/geometry/triangles/26601.txt'}