지쳐하다 (x). wrong 지치다 (o). correct [in terms of form] present/past tense 지치다/지쳤다. 피곤하다/피곤했다. [in terms of orgin] 지치다 : original korean adjective. 피곤하다 : chinese noun + 하다 = Korean adjective [In terms of meaning] 지치다 sounds like an action. 피곤하다 sounds like a status. get tired = 지치다, 피곤해지다. : action be tired = 지쳐있다. 피곤하다. : status Koreans are likely to use 지치다 rather than 피곤해지다 for action. Koreans are likely to use 피곤하다 rather than 지쳐있다 for status. In general, 지쳤다. past tense is used for the result in something. ex) I got tired of her. 피곤하다. present tense is used for current status. ex) I am tried now.

there is much diffrence between them. the base verb of "지쳐하다" is "지치다" and it's more stronger feeling than "피곤하다". i think it should be translated as "to be exhausted" rather than "to be tired". generally speaking, "지쳐하다" is not what you feel and it's kinda impression you've got in comparison with "피곤하다". "지쳐하다" is more like "지쳐(해) 보이다-to look exhausted" or "피곤해 보이다-to look tired". so we could say "그는 지쳐했다" - he seemed to be exhausted. Also, this word "지쳐하다" is often used as a past form "지쳐했다" in sentences.

normaly, 지쳤다 and 피곤하다 means same. but sometime 지쳤다 means 'I'm sick of~' for example, if you said, 'I'm sick of same working every day.' '난 매일 같은 일을 하는데 지쳤다.' you can said '지쳤다' but not '피곤하다' but if you said, 'I'm tired beacuse my work too hard.' you can said '지쳤다' or '피곤하다'. for example, '일이 너무 힘들어서 지쳤다.' or '일이 너무 힘들어서 피곤하다'.

the ovious difference 지쳤다 -> the pure korean word. 피곤하다 -> mixed with Chinese character. ( we call it 한자어(漢字語) which means the word derive from Chinese Character. ) 지쳤다 vs 疲困(피곤)하다. <<<<<< Anyway it's the same meaning. These days, some koreans don't use pure korean words because they think the word mixed with Chinese character sounds difficult so it's educated. but that's absolutely bullshit. I recommend you to use 지쳤다. This covers all what you wanna mean