Build a triangle from Angle Bisectors?

Three line segments (solid lines) intersect at a point. Could they be the angle bisectors of some triangle? You can use the sliders to set the lengths of the segments. Drag the R, G and B dots to fix the point at which the segments intersect and the angles between the segments. The dotted rays show the bisected angles at the points R, G and B. CHALLENGE: given three angle bisector lengths, locate the vertices and determine the size of the angles of triangles RGB. Can this always be done? Why or why not?