unit 1/2 geometry question.

[elpistachio107]

if ABCD is a cyclic quadrilateral and AB and DC are produced to meet at q, and BC and AD are produced to meet a R prove that QP and RP, the bisectors of the angles BQC and CRD respectively are  at right angles to each other. if you answer it could you please provide all reasoning and theorems 

[fun_jirachi]

if you answer it could you please provide all reasoning and theorems 

I was going to prompt you with hints, but this comment threw me off a bit; it seems like you want the full working out for whatever reason (I don't know why, but the connotations associated with such a request are generally bad). Note that such a practice does not help you understand geometry (and it's bad practice for studying anyway) since you just end up regurgitating an answer. There's also no evidence of an attempt on the question; have you had a go? If so, what have you come up with, what have you tried and where are you stuck? It's a lot more productive for us that answer questions on the forum and for your own learning that you've taken these initial steps prior to asking a question.

Nevertheless, here are a few general hints:
- Angle chasing is not an awful idea if you have run out of other ideas and theorems to test
- You can also try working backwards