Any triangle whose vertex is on the edge of the circle and has the diameter as the base is a right triangle. You can consider it a given.

Graphically, it's piss-easy to demonstrate it. Take your vertex, draw the line that starts from it, crosses the center of the disk, and mark a vertex where it touches the opposite edge. You now have 4 vertices, the original one, the one you just drew, and the two on the diameter. any quadrilatere with its diagonals of equal lengths, cutting each others in their middle is a rectangle, which means, right angles.