So I've been preparing for an upcoming high school math competition when I stumbled across the following optimization question on a practice test:
Henry and Daisy stand 14 ft apart, unmoving. Ed stands 10 ft from Henry and 8 ft from Daisy, forming a scalene triangle. What is the shortest distance Ed can move to form a right triangle?
So I know that I am supposed to minimize $\sqrt{x^2+y^2}$, where 'x' represents Ed's horizontal distance moved and 'y' represents Ed's vertical distance moved. However, I do not know how to find another equation using what they told me about the legs of the given scalene triangle. Given that the material of the these tests only requires knowledge up to AP Calculus BC, I suspect that the solution isn't too complex.
Ed must move along the radius of the circle having Henry and Daisy as endpoints of a diameter.