Basic Triangle Geometry on GRE: Length of one side of a triangle?

Question

Practice GRE problem that is giving me more trouble than it should. Why is the answer: 'The relationship cannot be determined?'

My answer was that the two quantities are equal--but that is clearly wrong.

Answer 1

The figures on the GRE are not drawn to scale. It is indeed possible that $IJ=5$ (if the triangle is equilateral). It is also possible that $\angle IGK < 60$ and so $IJ<5$. Since there is more than $1$ possibility, the answer is The relationship cannot be determined.

Also note that $\angle IGK$ can be more than 60 degrees and $IJ>5.$ In fact by the triangle inequality we have that $0<IK<20$ so $0<IJ<10$.

Answer 2

Draw a circle centered at G with r=10, you can pick up any point K on circle G, IK and IJ=IK/2 are changing pending on K's choice.