An Etymological Dictionary of the German Language/hagen
hagen, behagen, vb., from the equiv. MidHG. hagen, behagen, ‘to please, gratify,’ OHG. *bihagôn: comp. OSax. bihagôn, AS. onhagian, ‘to please, suit.’ The stem hag, ‘to suit,’ is widely diffused in OTeut., and its str. partic. is preserved in OHG. and MidHG. (gihagan and behagen, ‘suitable’). Allied to Scand. hagr, adj., ‘skilful,’ hagr, m., ‘state, situation, advantage,’ hœgr, ‘suitable.’ The root hag, from pre-Teut. kak, corresponds to the Sans. root çak, ‘to be capable, able, conducive,’ whence çakrá, ‘strong, helpful.’