I once heard that it is possible to reduce ligament pain by taking supplements (eg: glucosamine). I am looking for exercises to perform to strengthen the knees and avoid ligament injuries. Which exercises could help faster and better?
There is only anecdotal evidence to support the claim that taking supplements can help with joint pain. It appears to work for some people, and, not for others. There is, as yet, no scientific proof it works. As for exercises, I've had the unfortunate experience to rehab a torn ACL (Anterior Cruciate Ligament). As part of that rehab, I was instructed by the PT to perform certain movements with exercise bands. These exercises were designed to improve balance, stability, and strength of the supporting tissues. For example, I performed one legged squats with a resistance band. A simple web search should find more exercises for you.
I think this link will help you to strengthen your knee. Try it and do workout regularly and improve your diet and stay healthy.