c)
Mình gợi ý cách làm như sau:
$PBQI$ là hình bình hành
$\to E$ là trung điểm $BI$
Ta có: $\begin{cases}\widehat{MNC}=\widehat{MBI}\,\,\,\left(\text{ cùng phụ }\widehat{NCB}\right)\\\widehat{MNB}=\widehat{MBP}\,\,\,\left(\text{ cùng phụ }\widehat{MPB}\right)\end{cases}$
$\to\widehat{MNC}+\widehat{MNB}=\widehat{MBI}+\widehat{MBP}$
$\to\widehat{BNC}=\widehat{PBI}$
Mà: $\widehat{NBC}=\widehat{BPI}\,\,\,\left(\text{ cùng phụ }\widehat{BNP}\right)$
$\to \Delta NBC\backsim\Delta BPI\,\,\,\left( g.g \right)$
$\to \dfrac{NB}{BP}=\dfrac{NC}{BI}$
$\to \dfrac{NB}{IQ}=\dfrac{2NK}{2IE}$
$\to \dfrac{NB}{IQ}=\dfrac{NK}{IE}$
$\to \Delta NBK\backsim\Delta IQE$
$\to \widehat{NBK}=\widehat{EQI}$