Low-energy theorems for the cross sections of photo- and electroproduction of pions at threshold are obtained. The derivation of the theorems is based on the use of the PCAC hypothesis and on the expansion of the amplitudes in powers of k mint, q mint where k, q are pion and photon four-momenta and mint is some internal mass. All the contributions up to and including those quadratic in these ratios are taken into account. Two new low-energy theorems are obtained for the photoproduction cross sections. Predictions for electroproduction cross sections are given and it is shown that expected accuracy of these predictions depends crucially on the value of electron momentum transfer squared k2. For k2 ≪ mint2 the accuracy of the results obtained is higher than that of the calculations performed earlier. The possibility of determining pion and neutron radii through measuring electroproduction cross section and the cross section of reaction πN → Ne+e- is discussed. It is shown that the Born approximation which is currently used for this purpose is in fact inadequate to describe the amplitude and new model-independent formulae are presented which allow one in principle to determine the pion radius.