Triangle given the vertex A, the incenter I and the centroid G

1) Take M in AG such that AG = 2GM.
2) Take N in IG such that GN = 2IG.
3) Take A' in AM such that AM = MA'.
4) Draw the parallel from A' to AN.
5) Draw the circle with diameter IM.
6) These circle and line intersect at Q1, Q2.
7) The incircle has center I and goes through Q1 or Q2.
8) MQ1 (or MQ2) is a side, and the others are the tangents from A to the incircle.