∴AB=AE+BD=5
∵OD⊥BC,OE⊥AC,∠ACB=90
∴∠ODC=∠OEC=∠DCE=90
So ODCE is a rectangle.
OE = OD
∴ODCE is square.
∴CD=CE=OD=OE= radius r
∴AC=AE+r=3+r
BC=BD+CD=2+r
So Pythagorean Theorem: AB? =AC? +BC?
5? =(3+r)? +(2+r)?
25=9+6r+r? +4+4r+r?
r? +5r-6=0
(r+6)(r- 1)=0
R=-6 (truncated)
r= 1
The radius is 1.