This is in part why kat is so freelo when her dagger is on the ground it has a red zone around it to show its size (like MANY other champs abilities)
But Kats zones is the for the range of when SHE can put them up NOT that zone that will do damage. The Damage Zone is about 2x the size.
This is just bad design and inconsistent design.
1011001110006 votesThe damage that Katarina gets from picking up her daggers is not centered on the dagger but on Katarina.
Katarina's passive deals damage in a 340-unit radius around Katarina, about 2-3x farther than a melee auto range, or 3 Teemos.
INT then ULT5 votesGimme old 
skittles back.
Akali is SO HOT3 votesThe circle is just there to show how close Kat needs to be to pick up the daggers. If you are referring to putting a range indicator for her passive damage, there's no point in doing it for an ability that lasts for less than half a second.
Bonipherus1 votesThe actual range on daggers is really,really large because she can click anywhere around that circle and jump to it to deal damage. She can click on the very edge of any part of the circle and deal damage 340 units away from that circle which effectively makes her damaging zones gigantic. In short, don't trust her shown dagger area as a small spot to avoid and instead treat the area like an Anivia ult and don't go anywhere close to it.
