You can solve this easily and with a clean topology by keeping it all quads.
Just create a "quad corner" around the radial part, where quads meet at a three-edge vertex.
Start by extruding one of the "center edges" from the radial part so it meets the adjacent one. Then extrude one of the remaining ones, and place it so the quads meet at the center and match perfectly (Use Ctrl snapping to aid in precise placement if necessary).
Repeat the process for the opposite edge , you can quickly create a new face between the two existing edges by pressing F.
You you then end up with a two edge gap you can easily bridge to the remaining edges with the Bridge Faces operator, B key.
Don't forget to W > Remove Doubles at the end, to merge together all newly created geometry.
For more info consult this comprehensive Topology Guide