The difference between being keen on doing sth and being keen to do STH

Being keen on is keen on: Mrs. Miller is very keen on art.
Mrs. Miller is very interested in art.

be eager to do something: be keen on doing.../be keen to do ...
She very keen on visiting.
She very keen to visit.
She is eager to visit China. Be keen to do sth desire to do sth be keen a for SB. Do
STH strongly ask someone to do something keen on sth keen on something be keen on doing 
sth like doing sth The thing 
is keen on SB like someone 

P:keen to refers to "desire, very much", generally indicates that they have not achieved the desire and unfinished business. Keen on refers to "love, passion." "
Example: 1. The boy is keen to the sea. 
The child is very interested in sailing.
2..He is keen on angling. 
He likes fishing.