Okay, here's what I have so far:

The slope of the ladder would be rise over run, making the slope .

The derivative of the hypocyloid would start out to be:

but how can I take the derivative of two things at once? I would need the speed in the x or speed in the y wouldn't I? To prove they these two things were tangent, I'd have to make the slopes equal, right?

Nevermind, got it!