$\text{CIRCLE}$ is related to $\text{RICELC}$ in the same way as $\text{SQUARE}$ is related to:

Let us look at the positional changes of the letters from $\text{CIRCLE}$ to $\text{RICELC}$:
The positions of the letters in ${\text{C}}_1{\text{I}}_2{\text{R}}_3{\text{C}}_4{\text{L}}_5{\text{E}}_6$ are rearranged to form ${\text{R}}_3{\text{I}}_2{\text{C}}_1{\text{E}}_6{\text{L}}_5{\text{C}}_4$.
The logic splits the 6-letter word into two equal halves of 3 letters each and reverses them independently:

* First half: $\text{CIR}\to \text{RIC}$
* Second half: $\text{CLE}\to \text{ELC}$

Applying the same pattern to $\text{SQUARE}$ (${\text{S}}_1{\text{Q}}_2{\text{U}}_3{\text{A}}_4{\text{R}}_5{\text{E}}_6$):

* First half: $\text{SQU}\to \text{UQS}$
* Second half: $\text{ARE}\to \text{ERA}$

Combining them gives $\text{UQSERA}$.