Established in Brussels by Louis Mettewie in 1885 as Société des Cycles et Automobiles Belgica, their first car was was exhibited at the Antwerp salon in 1901.
Belgica built single and twin cylinder motorcycles and also a four.
Also known for their bicycles, they moved from Brussels to Zaventem before ceasing production in 1909. The firm was absorbed by the Belgian automobile maker Excelsior.
Louis Mettewie was dismissed from his position in goverment for his support for universal suffrage. He founded two periodicals. He founded the Chambre Syndicale des Constructeurs d'Automobile and organised the first motor shows in Belgium in 1902, 03 and 04. Mettewie was mayor of his municipality for 20 years.
Sources: Wikipedia NL, fr.wikipedia.org.
Notes. 1. Comments on the 1911 image indicate that it may not actually be a Belgica motorcycle... "... on the back cover of the 1911 catalog of the firm "La Belgica", dealer in Belgium of the German cycles Büffel, Zoller, Militaria and Salvator, appears the reproduction of a small motorcycle..."
To which Etienne Piron replies: "It's also possible that the motorcycle only exists in drawings and there was never a "La Belgica" motorcycle..."
So it would seem that this motorcycle is advertised by a different firm, possibly with the same name. Addresses certainly don't match.
