[franze]

interesting question, near perfect triangles

  07:18:18 
  16:41:41 
  09:23:23 

but non of them are mathematically perfect triangles.

well 00:00:00 and 23:59:59 are

for a perfect triangle all three hands need equal distance from center. hours range 0 to 23, minutes and seconds 0 to 59, so you need

h(divided by) 23 to equal

m(divided by) 59 to equal

s(divided by) 59.

since 23 and 59 are both prime, bad luck.