Question 41
Squares $ABC'C''$, $BCA'A''$, $CAB'B''$ are constructed on the outside of the sides of the triangle $ABC$. The line $A'A''$ meets the lines $AB$ and $AC$ at $P$ and $P'$. Similarly, the line $B'B''$ meets the lines $BC$ and $BA$ at $Q$ and $Q'$, and the line $C'C''$ meets the lines $CA$ and $CB$ at $R$ and $R'$. Show that $P$, $P'$, $Q$, $Q'$, $R$ and $R'$ lie on a circle.