which muslim ruler born a nomad, established an empire that eventually spanned three continents - Asis, Africa, and Europe?

Answer: A. Osman.

Osman was the founder and ruler of the Ottoman Empire which controlled most parts of Southeast Europe, Western Asia and North Africa between the time period of 14th and early 20th century.

This empire was founded at the end of the 13th century in the town of Söğüt in northwestern Anatolia. The Ottoman Empire was a multinational and multilingual empire. Constantinople was the capital of this empire.