Matching sizes of a one-draw and a two-draw test

$X_1,X_2$ are i.i.d. uniform on $[\theta,\theta+1]$. To test $H_0:\theta=0$ versus $H_a:\theta>0$, test A rejects when $X_1>0.95$ and test B rejects when $X_1+X_2>c$. Find $c$ so that both tests have the same significance level.

$c=2-\sqrt{0.1}\approx1.68$. Test A has $\alpha=0.05$. Under $H_0$ the sum has a triangular density on $[0,2]$, whose upper tail beyond $c\in[1,2]$ is $\tfrac{(2-c)^2}{2}$; setting this to $0.05$ gives $2-c=\sqrt{0.1}$.