Problem:
A angle-angle-side triangle has angles $124 {}^{\circ}$ and $51 {}^{\circ}$ and a side of length $\frac{5}{2}$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, and symmedian point of the triangle.
Answer:
Centroid: $\left\{-\frac{5}{12} \sec (34 {}^{\circ}) (\cos (17 {}^{\circ})-3 \sin (5 {}^{\circ})),\frac{5}{6} \cos (39 {}^{\circ})\right\}$ 
SymmedianPoint: $\left\{-\frac{5 \sin (5 {}^{\circ}) (\cos (29 {}^{\circ})-3 \cos (39 {}^{\circ})) \cos (39 {}^{\circ}) \sec (34 {}^{\circ})}{2 (\sin (12 {}^{\circ})+\sin (22 {}^{\circ})-\cos (10 {}^{\circ})+3)},\frac{5 \sin ^2(5 {}^{\circ}) \cos (39 {}^{\circ})}{\sin (12 {}^{\circ})+\sin (22 {}^{\circ})-\cos (10 {}^{\circ})+3}\right\}$ 
Incenter: $\left\{\frac{5 \sin (5 {}^{\circ}) \cos (39 {}^{\circ}) \sec (34 {}^{\circ}) \left(\sqrt{2}-\sqrt{\sin (22 {}^{\circ})+1} \tan (34 {}^{\circ})\right)}{2 \left(\sqrt{2} \cos (39 {}^{\circ})+\sqrt{\sin (22 {}^{\circ})+1} (\sin (5 {}^{\circ}) \sec (34 {}^{\circ})+1)\right)},\frac{25 \sin (5 {}^{\circ}) \cos (39 {}^{\circ}) \sec (34 {}^{\circ})}{4 \left(\frac{5 \cos (39 {}^{\circ})}{\sqrt{2 (\sin (22 {}^{\circ})+1)}}+\frac{5}{2} \sin (5 {}^{\circ}) \sec (34 {}^{\circ})+\frac{5}{2}\right)}\right\}$ 
Orthocenter: $\left\{-\frac{5}{2} \cos (39 {}^{\circ}) \tan (34 {}^{\circ}),-\frac{5}{2} \sin (39 {}^{\circ}) \tan (34 {}^{\circ})\right\}$ 
Circumcenter: $\left\{\frac{5}{4} \sin (5 {}^{\circ}) \sec (34 {}^{\circ}),\frac{5}{4} \cos (5 {}^{\circ}) \sec (34 {}^{\circ})\right\}$ 
NinePointCenter: $\left\{-\frac{5}{8} \sec (34 {}^{\circ}) (\cos (17 {}^{\circ})-2 \sin (5 {}^{\circ})),\frac{5}{8} \sin (17 {}^{\circ}) \sec (34 {}^{\circ})\right\}$
{'source': 'AMPS', 'file': 'amps/mathematica/geometry/triangles/81582.txt'}