Malfatti circles

1) Let I be the incenter of ABC. Draw the incircles ca, cb, cc of IBC, IAC, IAB.
2) Two of these circles have two internal common tangents: as exemple, cb and cc have IA and a new line a. Draw these lines a, b, c.
3) The circle tangent to AC and BC and also to a and b is a Malfatti circle.