The sentence:

The common value of the products is then depends only on P and the circle and is known as the Power of Point P with Respect to the Circle.

Should probably read:

The common value of the products depends only on P and the circle and is known as the Power of Point P with Respect to the Circle.

The sentence:

The convenience is in that it now it is possible to tell points inside the circle from the points outside the circle.

Should probably read:

The convenience is that it is possible to distinguish points inside the circle from those outside the circle.

I appreciate the collection you have made available. I hope you';; find my notes useful.

I do and appreciate your taking the time.

Many thanks,
Alex