A system for and method of applying non-invasive brachytherapy to a targeted volume within a protruding organ of a patient, employs an applicator constructed so as to be positioned relative to the organ so that an enhanced dose of divergent radiation is deliverable from at least two locations at or very near the periphery of the organ transcutaneously to the targeted volume of the protruding organ from at least two directions so that a higher dose is delivered to the targeted volume than to tissue surrounding the targeted volume. The treatment planning, and image guidance techniques are also described.