The infographic below shows a triangle ABC
with cevians BD and BE. If the incircles O1, O2, and O3 of the
triangles ABD, DBE, and EBC, respectively, are equal, prove that
the incircles Q1 and Q2 of the triangles ABE and DBC are equal.
A cevian is a line segment with one endpoint on a vertex of a triangle and the other endpoint on the opposite side.