Mrs. Napier's Detention

The reason that most students kept quiet and pretended to listen in Mrs. Napier's math class was because everybody feared her detentions. Mrs. Napier's detention didn't involve merely sitting in her room for half an hour after school. Serving a detention for Mrs. Napier involved solving a single math problem that she selected from what she affectionately called her own "Pandora's Box." I served only one detention that entire year, as the first experience taught me to never earn another. At the beginning of that detention, Mrs. Napier gave me a sheet of paper on which she had drawn a circle with twelve distinct points. I was instructed to draw as many distinct triangles as could be formed with vertices at the given points. How many triangles did I have to draw?