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Perfect.
Big muscles are not necessarily the key to performing body-weight feats of strength - you need look no further than my 165 pound frame for evidence of that. The key is core strength and total body control.
It's hard to get a consensus on what counts as the definitive one arm push-up. There are different variations, and like all other feats of strength from the pull-up to the human flag, everyone has their own opinion.
I believe that the ideal range in somewhere between 90-110 degrees of flexion as measured along the OUTSIDE of the elbow, depending on the mobility of the individual. If you aren't sure how low you are getting, have someone else watch you. Sometimes it's hard to feel how your body looks when you exercise. People often think they are going lower than they actually are. I know - I was once one of them! In order for me to count a rep in any sort of competitive situation, I would need to see a minimum of 90 degrees of flexion.

A strong midsection helps to get your whole body to work together. You also need to think about your opposite leg; If you are doing a one arm push-up on your right arm, your left leg needs to be engaged and vice versa. I find it best to practice keeping my whole body tight during the entire range of motion.
A great way to practice the technique of the one arm push-up is to perform it up on an angle by using a bench or bar that's a few feet from the ground. Using paralettes or push-up bars can also be a good tool for practicing technique once you get closer to the real deal.
...and beyond
There's a lot of new challenges that lie ahead once you get the hang of the one arm push-up, like plyometric one arm push-ups, one arm push-ups on a medicine ball and the one arm/one leg push-up. With so many ways to vary this classic you can keep your workouts fresh and challenging!
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