you can find the radius of the smaller circle using this method(please view diagram)
Large circle radius 10cm
Medium circle radius x
Small circle radius Y
(sq)AB=(sq)2X+(sq)2X=(sq)4x+(sq)4X
(sq)AB=(sq)8X
AB=2(sqrt)2X
2X+2Y=2(sqrt)2X
AB=2x+2Y
20=2X=2Y+2X=4X+2Y
2Y=20-4X
Y=10-2X...