∵向量OA*向量OB=0,
∴|OC|²=λ²|OA|²+μ²|OB|²+2λμOA·OB
= (λa)²+(μb)²
∵a²+b²=4,a=2cosα,b=2sinα
∵（λ-1/2)²a²+（μ-1/2)²b²=1
(λ-1/2)a=cosβ,（μ-1/2)b=sinβ
λa=cosβ+cosα,μb=sinβ+sinβ
∴ (λa)²+(μb)² =(cosβ+cosα)²+(sinβ+sinβ)²
=2+2(cosαcosβ+sinαsinβ)
=2+2cos(α-β)≤4
∴|OC|≤2,则|OC|的最大值为2