Is this man flirting with me?

I want to know if my doctor is flirting w me. Everytime I go in, he seems especially happy to see me, and on one occasion I emailed him to see if I should come in for an appointment, for a simple infection that he already knew what it was b/c of the symptoms i gave him, and it couldve been treated with an anitbiotic given over the phone. He said, 'yes come see me', and when i got there the next day, he walked past my room while helping the person before me, and doubled back once he saw me and peeked his head in and said 'hey there!' really enthusiastically with a huge smile. then since he didnt have a thermometer on hand, to see if i had a fever, before he went to get a thermometer, he put his arm around me to see if I was warm. then after I leave everytime, he puts his hand on my back and leaves it there. then he always brings up commonalities between us, and never leaves any room for silence. like how he was supposed to go see my school's team play in the playoffs the next wkend (which was located hours and hours away), but couldnt cause he had to work, or how he responds to my emails so quick (just to name a few.) he also said ';email me if you need anything while your away!'; i dont know what to think. he has a daughter 2 years younger than me, and I know from a friend who has a parent that works with him that his wife just gave him divorce papers. (he never talks about the wife) I'm obviously not looking for a relationship out of it, I just want to know what the intentions are, (kind of have a crush on him) and if i'm reading him correctly...and I think it'd be fun to flirt back and see what happens. The age doesnt bother me (me, 21, him 46) and I want to know how to flirt back, because I know that even if they are interested they cant really make the first move because of doctor/patient rules.





dont need any criticisms and not looking for a relationship or to break up a family. just trying to get my facts straight and get some advice on how to actIs this man flirting with me?
unless he does something really obvious, like asking you out, yo can never tell, some people are just always that enthusiastic and friendly, but others are not, you'd have to find out how he acts around others, only then you could compare. But then again maybe yo just seem so nice and friendly that he acts more nice around you, for a simple reason that you give him a positive impression.