$\mathbb{\text { Franklyn } 5 . P .}$

Let \$A_1A_2A_3\$ be an acute triangle, the radius of the circumscribed circle is $\$ 1 \$$, \$O\$ is the center of the circumscribed circle. From the vertices \$A_i\$ the cevians are drawn through \$O\$ to their intersections with the opposite sides at points \$B_i\$ respectively $\$(\mathrm{i}=1,2,3) \$$.

(a) Among the three segments \$B_iO\$, choose the longest one. What is its smallest possible length?

(b) Among the three segments \$B_iO\$, choose the shortest one. What is its largest possible length?