I started a thread just like this 3 or 4 years ago when attempting to put my first Goped motor back together. Broke the first set, ordered a second and broke those too. When you're doing it, pretend those rings are made of pencil led. They break almost as easily. Slide that head over REAL gentle-like.
Finally, someone on GPN told me to cover the piston & cylinder in 2-stroke oil first if it's been sitting out for a long enough period of time for them to get kinda dry. Never broke a ring since.
You'll need a steady hand and a lot of patience the first time. Do them one at a time. Find the little stuck out dimple thing in the piston (rotate the ring to find it) and squeeze, then gently press over the cylinder. Then do the second (the dimple is usually in a different location for both rings). It's a pain, but it just takes practice.
BTW: If that's just been cleaned then I'm guessing you scraped a lot more than that amount of gasket off the base in the pic. Now is the best time to replace it if it needs replacing, as I'm sure you wont be thrilled to pop that sucker back when the motor ends up with an air leak.