correction, my proof does use similar triangles. i found a mistake in my proof and had to fix it.
(hehe, oops)
um, i haven't got the hang of Latex, so i hope you don't mind if i give you a link to a pdf file instead. (you'll have to download it, sorry!)
although i think and am more fluent in English, i always solve math problems in Vietnamese, so my proof is basically a literal translation of what i would've written in Vietnamese, so I'm sorry if it doesn't make sense in some parts. All symbols are what the Vietnamese use in our math, if there is anything different from what most people would write please tell me.
once again, sorry for making you download a pdf file.
my proof