Online Geometry Problem 772: Similar triangles with a Common Vertex,
Equal Angles, Midpoints, Metric relations. Level: High School, College,
Mathematics Education

The figure below shows triangles ABC and
AB'C' with the common vertex A, angle BAC = angle B'AC', and angle
ABC=AB'C'. Points D, E, F are the midpoints of BC, B'C, and BC',
respectively. If AB = 5, AC = 6, and DE = 4, find DF.