9 Point circle of 3-4-5 right triangle

This was a question in the urgent help section, but I figured out what I needed, so if a mod could delete that thread, or lock it, that would be appreciated.

I'm just trying to understand something on a problem. It states that a 3-4-5 right triangle has 5 distinct points defining it's 9 point circle. However, whenever I try to draw this out, I only get 4 points.

Someone else emailed the professor about this (The professor wrote 8 instead of 5), but that person found 5 points, and the professor said it should be 5 points. Any insight into what I may be doing wrong?

These are the points I got.

1)Midpoint (c), Euler (b) are the same

2)Altitude (b), Altitude (c), Euler (a), A, H, are all the same

3)Midpoint (b), Midpoint (c) are the same

4) Midpoint (a), Altitude (a), O, are all the same.

Thanks!