Low pass and high pass \$RC\$ filters have a cutoff frequency that is equal to $$f_c=\frac{1}{2\pi RC}$$ This should be the frequency at which the ratio \$|V_{out}/V_{in}|\$ is equal to \$1/\sqrt{2}\$.
But how can I have at the same frequency the same ratio \$|V_{out}/V_{in}|\$ measuring \$V_{out}\$ firstly across capacitor and then across resistance?
KVL states that \$V_{in}=V_{resistance}+V_{capacitor}\$ at any time, but if at \$f_{c}\$ we have \$V_{resistance}=V_{capacitor}=(1/\sqrt{2}) \, V_{in}\$, then KVL would not be respected!
I'm surely missing something but I really can't see how the definition of cutoff frequency is consistent with KVL. Any help is highly appreciated