Quote Originally Posted by Del Murder
even though I still couldn't prove why that angle is a right angle.
In your picture, we know that the (b/2)(8-h)z triangle is a right triangle. And with the problem solved we know that b/2=2√3 and that 8-h=2, therefore z=4. Also with the problem solve one can also derive that c=4√3. So (d=diameter), if the zcd triangle is a right triangle, then the Pythagorean theorem should work. And behold 4² + (4√3)² = 8². Therefore, zcd is a right triangle. Without having solved the problem I'm sure you can do what Kirobaito did and put everything in terms of h and use the same logic as above.