Read Li I Yu's Five Character Secret and you will find a reference to strengthening the thighs.
So why do you need strong thighs, indeed, strong legs?
This is so the legs can absorb the relaxation of the torso, which then feels light and nimble. The legs also need to relax so the relaxation goes down to the feet. The feet in turn relax not so everything can press into the floor because that is a one sided view.
The ground comes up through the lower limbs into the torso and out to the arms,or for a kick directed into the leg so you are creating a conduit. Slow practise sets up the neural pathways.
This is not a quick thing and requires concentrated practise. As you relax into the legs they complain and I often felt like my legs were leaden. Actually this never seems to end!
As we get older our balance and leg strength can deteriorate so I feel that Tai Chi is a fantastic health promoting activity in this regard.
When you start Tai Chi there is a lot of advice to turn the waist. We are told the waist is not the same as what we think of as the waist but then no one tells you what it is.
So you think of turning from the hips but that's not it. Nor is it turning from the Dan Tien. I remember my late teacher John Kells telling us in class that "what is the waist" was a burning question for him. Eventually he came to the realisation that it was the lumbar spine, like an iron bar and that you turned from there.
Since then a lot of Chinese writings on tai chi have been translated which give detailed information about the waist. which is defined as the Yao. This encompasses the lumbar spine as well as the muscles and tissues around it and this is the area that you turn from, but not like a brick.