Right Triangle inscribed in a circle

Yes always

jus a little proof:

lets assume that the hypotenuse in not always the diameter and we will later contradict this.
see the image
let line CD is the hypotenuse and angle COD=90
let AB is the diameter, so we know that angle AOB is 90
as you can see
both the angles AOB and angle COD can be equal only when AB=CD
so that contradicts our assumption.
May be not the exact prrof u were looking for, but still..

Thanks a lot.

Can anyone point me to some resource summarizing such theorems. Especially related to cicrumscribed and inscribed circles.

Madhur