Geometry Problem 1388: Triangle 40-60-80 degree, Incenter, Congruence

Proposition

A-B-C is a 60-80-40-degree triangle, respectively with I as incenter. Prove that CI = AB.
This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka.
 

Geometry Problem 1388: Triangle 40-60-80 degree, Incenter, Congruence