Problem:
A triangle has sides $\frac{21}{2}, \frac{15}{2}, 4$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, and symmedian point of the triangle.
Answer:
SymmedianPoint: $\left\{\frac{298}{365},\frac{56 \sqrt{11}}{365}\right\}$ 
Centroid: $\left\{-\frac{1}{4},\frac{7 \sqrt{11}}{12}\right\}$ 
NinePointCenter: $\left\{-\frac{11}{8},-\frac{9}{8 \sqrt{11}}\right\}$ 
Circumcenter: $\left\{2,\frac{43}{2 \sqrt{11}}\right\}$ 
Incenter: $\left\{\frac{1}{2},\frac{7}{2 \sqrt{11}}\right\}$ 
Orthocenter: $\left\{-\frac{19}{4},-\frac{95}{4 \sqrt{11}}\right\}$
{'source': 'AMPS', 'file': 'amps/mathematica/geometry/triangles/92295.txt'}