  A new method is proposed to deduce the neutron radii of neutron-rich nuclei.
This method requires measuring the reaction cross sections of both the
neutron-rich nucleus and its stable isotope at the same energy on a proton
target. Using this method and the available experimental data of $^{12,22}$C +
$p$ and $^{9,14}$Be + $p$ at 40$A$ MeV, the neutron radii of $^{22}$C and
$^{14}$Be have been deduced for the first time.
