All the things - oh but ALL the things NightNightBadger said.
I'm typing this sitting on a pillow on top of my memory foam mattress. Because for me BMI 16.5 apparently means an incredibly bony back & bottom. Partly, mostly, maybe, even this time around, this is due to my physical disability, but having developed anorexia at 10 I have actually spent (just) over two thirds of my life where the most well I've been is the times I've achieved Putting The Fun In Functional Anorexia (or at times, when medication made me gain weight, EDNOS [anorexia] - that'd be a subset of OSFED now I know but no idea what).
I didn't get treatment when I was younger. If I ever see the utter cretin from CAMHS who assessed 12/13yo me after my father found my packed lunches rotting under my bed I might drown her in a vat of (soya+fibre, ofc) tubefeed. Either she BELIEVED my "I didn't want to hurt Daddy's feelings by not eating them & I didn't want anyone to see me throw them away" (tbf, I DIDN'T want to worry him...) spiel, or she somehow felt it was appropriate to adopt the approach you use with adults (ie unless hugely medically compromised treatment must be actively sought by the individual). Whichever one, she was a blithering idiot. She apparently bought my "oh yes, I'm very happy; I love my school; I've got so many friends; no, no problems at all!" Happy people being well-known for their defensive posture, lack of eye-contact, flattened affect & INSANE startle reflex. White, just scraping into my teens & the middle class, super academic over-achiever but hyper self-critical, just been through MAJOR trauma: frankly it would have been more surprising if I didn't develop anorexia given those demographic tickboxes.
I was hellbent on clinging to my eating disorder. I would, I can tell you know, have physically fought anyone who tried to make me eat. My anorexic!friends (we huddle together for warmth...) who received treatment as children/teens say that they were mostly utterly vile to their families for at least some of it - but in the back, behind the lashing out, there was always a part of them, somewhere, desperate to be reached & helped & held. Often being quite shocked by their own behaviour at that. Because eating disorders drive you to all sorts of things.
Please, OP, don't let her tell you she's fine. And hang in there through the kicking & screaming. Loath as I am to suggest an invasion of privacy, I think it's worth trying to find out if she has a proana instagram/tumblr or an account somewhere like "my pro ana dot com" (I'm not putting in a link because I don't want this thread coming to their attention, OP has more than enough on her plate & I don't need accusations of treachery/clearly not REALLY being anorexic 🙄/not understanding the site is all peace & love & fluffiness [it is FAR better than old-style proana & even than it used to be, but it would be HUGELY damaging to a vulnerable young person - NB I'm not a member there]).
b-eat can offer both you & your daughter help & support alongside whatever treatment she receives... If you're able to do so, I strongly suggest accessing private treatment for her - NHS services are just so desperately overstretched. The BACPS website has a therapist-finder section & you can (IIRC - a friend was telling me how clients find her, sadly I've not the money for private treatment) narrow it by specialty as well as area, so you could specify someone who treats teens & children as well & who works with ED patients. There are also therapists who list specialisms like working with performers - they see a lot of ED patients because anorexia continues to be rife in dance!world: there was an audition at the studios where I do ballet today & one girl said to another "I was too fat when I got the call so I've just not eaten anything for 2 days" & the other replied "you've got to do what works". Resisted the urge to turn round and shout "BOO!" at the ones who commented my back actually looked scary skinny & they were glad THEY weren't ballet dancers, you have to be even thinner than for musical theatre & commercial stuff. Lovely...
Sorry. I'm babbling. And digressing. I'm just... I know it must be frightening & overwhelming for you OP. And I'm very sorry, but it's going to be worse-before-better with some truly monstrous performances from your daughter unless she's a first amongst ED'd teens. But you WILL get through it. And tackling it now means that you are giving her a chance at having a life as a normal, functioning adult. Because even if an eating disorder doesn't kill you physically, living with one for years on end is not only soul-destroying but it circumscribes your very existence. Too tired to see people, can't concentrate to read/watch a film/knit/hold a proper conversation, can't wear swimwear on a beach or generally dress exactly how you want - your ED chooses your clothes, can't go to meals with people, no birthday cake, physical issues like poor circulation & brittle bones, hiding indoors when it's cold, feeling driven to exercise obsessively... It's an existence rather than a life & I wouldn't wish it on anybody.
One last thing before I lame duck into the wings: don't feel bad you didn't notice. Weightloss will have been gradual and (certainly as it progressed) deliberately concealed; and all sorts of subterfuge & shenanigans going on with food [& the avoidance thereof]. You haven't messed up. You've realised now & you're going to do something (rather than ostriching about it until your daughter collapses on public & has to be admitted - saves you a row, but does, you know, almost result in her death so POSSIBLY NOT WORTH IT ahem... sorry...)
Am sure there will be lots of people who will be able to tell you about successfully getting treatment for their children. Am a bit surprised in a way MN doesn't have A Thing for it. I'm not sure exactly what where, mind you...
Right. That's it. Past bedtime. Please let us know how it goes, won't you? I will cross my fingers & hold my thumbs for you.
(And I know hugs are utterly infra dig here, but I'm just leaving a little pile of them here. Should you happen to need them.)