$ OK. $
First we draw a second tangent from P to $ \omega $ named $ PG $ . Here, $ PG||MR||AE $ (it can be showed easily).
We let, There is $ P_{\infty} $ on the line $ PG $ . Now, $ PMNP_{\infty} $ is a quadrangle & $ E , F $ are the tangent or contact point of $ MP $ & $ NP_{\infty} $ resp to $ \omega $ . So, by the converse of brianchon's quadrangle theorem , we can tell $ PMNP_{\infty} $ is inscribed about $ \odot (O) $ as $ PN,MP_{\infty},EF $ are concurrent . For this, $ MN $ is tangent to $ \omega $ $ as follows $ $ .........[proved] $