Giải thích các bước giải:
Ta có :
$\begin{split}\widehat{POQ}&=\widehat{POM}+\widehat{MOQ}\\&=\dfrac12\widehat{DOM}+\dfrac12\widehat{MOE}\\&=\dfrac12\widehat{DOE}\\&=90^o-\dfrac12\widehat{BAC}\\&=\widehat{PBO}\\&=\widehat{OCQ}\end{split}$
Mà $\widehat{QPO}=\widehat{OPB}$
$\to\widehat{POQ}+\widehat{QPO}=\widehat{PBO}+\widehat{OPB}$
$\to \widehat{PQO}=\widehat{POB}=\widehat{OQC}$
Lại có : $\widehat{PBO}=\widehat{OCQ}$
$\to\Delta PBO\sim\Delta OCQ$
$\to\dfrac{PB}{OC}=\dfrac{BO}{CQ}\to BP.CQ=OB.OC=\dfrac14BC^2$