Chemically Induced Dynamic Nuclear Polarization (CIDNP) of the diamagnetic products of radical reactions is exploited for the purpose of determination of the hyperfine coupling constants (HFCCs) of the radical intermediates. A simple proportionality relation between geminate CIDNP of a nucleus and its HFCC at the radical stage is established. The applicability range of this relation is determined: the relation is fulfilled in the case of a large difference in g-factor between the radicals involved and for the situation where the number of magnetic nuclei in the system is sufficiently large. The validity of the relation was confirmed by CIDNP experiments on radical pairs with precisely known HFCCs. Using the proportionality relation we were able to measure the HFCCs in various short-lived radicals of the amino acids histidine and tryptophan and of the S-N-centered cyclic radical of methionine derived from the methionine-glycine dipeptide in aqueous solution.