Problem 690: Distance between the Incenter and the Centroid of a Triangle

Proposed Problem
Prove that the distance between the incenter I and the centroid G of a triangle ABC is:
Click the figure below to see the complete illustration.


See also:
Distance between the Incenter and the Centroid
Level: High School, SAT Prep, College geometry

Elearn Geometry Problem 196: Inradius and Exradii Formula

See complete Problem 196 at:
www.gogeometry.com/problem/p196_triangle_inradius_exradius_formula.htm

Triangle: inradius and exradii formula. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.