Anatoly Liberman, Between beriberi and very, very: In Praise of Useful Waste, Or, Tautological Compounds, discusses words composed of two roots that are synonymous, such as pathway and sledgehammer. He remarks, "It is to be regretted that no one thought of compiling a dictionary of these compounds in the languages of the world."
If anyone ever does compile such a dictionary, perhaps circumambient and circumambulate (neither mentioned by Liberman) should be entries in it. In these words derived from Latin the elements circum- and -amb- both mean "around." Words related to the Latin preposition circum are common in English, such as circuit, circle, circus, etc. In Latin, amb(i)- occurs only as a prefix. Roger D. Woodard, Indo-European Sacred Space: Vedic and Roman Cult (Urbana: University of Illinois Press, 2006), p. 159, lists ambages, ambio, ambulo, amfractus (anfractus), and anquiro among Latin words formed from amb(i), and his list is not exhaustive. From ambio comes ambitio, "going around," especially to canvass votes, whence English ambition.
Greek equivalents of circum and amb(i)- are περί (peri) and ἀμφί (amphi). These roots occur in many English words, such as peripatetic and amphitheater. In the Greek-English Lexicon of Liddell-Scott-Jones I find over a dozen words starting with ἀμφιπερι- (amphiperi-), including ἀμφιπερικτίονες (amphiperiktiones) = dwellers all around, and two starting with περιαμφι- (periamphi-) — περιαμφιέννυμι (periamphiennumi = clothe on all sides) and περιαμφίς (periamphis = turning round and round). All of these are tautological compounds.