Enlightenment325

This is a question that has been perplexing me for a number of years. Unfortunately, I don't have the experience with geometry to answer it myself, so I am hoping someone here can help.

Note: No this is not homework help - It's the basis for another idea that's been percolating around in my brain, which I may add to the end of the thread, assuming this turns out the way I expect.

Let us suppose we have a right triangle, ABC, with sides AB and BC, and hypotenuse AC.

 

If we draw one line that bisects and is perpendicular to AB and another that bisects and is perpendicular to BC, will the intersection of those lines fall exactly on AC?

Yes it will. In a right triangle, the circumcenter always lies on the hypotenuse.