April wrote: Find the locus of excenters of right triangles with given hypotenuse. The locus are two arcs $ 45^o$ which are set up on the hypotenuse.

can u explain how are the arcs setup ?

Sorry for reviving this old thread. mathiee wrote: can u explain how are the arcs setup ? The arcs are subtended on the either sides of the hypotenuse such that the given hypotenuse subtends $45^{\circ}$. And also the locus is points bounded by the extreme points on the hypotenuse.