A circle puzzle

Tease your brain

How much do you know about circles? Does the Pythagorean theorem sound familiar? How about inscribed angles and their corresponding central angles? Know the area of a sector?

Here's a circle puzzle that was recently passed along to me by a friend. The task? Figure out the radius. Only two measurements are given (unless, of course, you count the right angles): the hypotenuse of a right triangle inscribed in one quadrant of the circle and the distance of one vertex from the circumference of the circle. Believe it or not, that's plenty of information.


So: what is the radius? The friend who sent me the puzzle said he saw “a horrendous variety of wrong solutions/answers/guesses.” Want to contribute to the variety?

Don't worry. I'm not giving the answer away all at once. Go read the comments. You'll probably find an answer there soon enough. And if you don't provide it, I'll post it myself.