Create an arc on an arc at a specific location

[brwoodhouse]

First, I don’t know how to measure along an arc. Second, I don’t know how to drop a point at the spot I need without drawing a line. I tried drawing a straight line but I can’t get it to land on the arc and I can’t rotate it to land on the arc without changing the shape of the bema. I’m sure it’s a simple fix but I’m not super knowledgeable in ketchup .