Triangles from Nine Points

Difficulty: Medium · Topics: Discrete Mathematics, Combinations, Geometry

In the figure, A, B, C, D, E, F, G lie on the circle, and G, H, K, C lie on one line.

graph "x":[-3.0,3.2],"y":[-2.7,2.7],"axes":false,"ink":true,"label":"Seven points A to G on a circle; a line through G and C also passes through the inside points H and K","items":["type":"circle","at":[0,0],"r":2,"type":"line","from":[-2.711,-1.083],"to":[2.02,2.108],"type":"point","at":[-1.147,1.638],"label":"A","anchor":"nw","type":"point","at":[0.0,2.0],"label":"B","anchor":"n","type":"point","at":[1.231,1.576],"label":"C","anchor":"ne","type":"point","at":[1.981,-0.278],"label":"D","anchor":"e","type":"point","at":[0.0,-2.0],"label":"E","anchor":"s","type":"point","at":[-1.286,-1.532],"label":"F","anchor":"sw","type":"point","at":[-1.923,-0.551],"label":"G","anchor":"w","type":"point","at":[-0.882,0.151],"label":"H","anchor":"se","type":"point","at":[0.159,0.853],"label":"K","anchor":"se"]

At most how many different triangles can be drawn with these points as vertices?