Question 62
The incircle of a triangle $ABC$ touches the sides $BC$, $CA$, $AB$ at points $D$, $E$, $F$, respectively. Let $X$ be a point on the incircle, different from the points $D$, $E$, $F$. The lines $XD$ and $EF$, $XE$ and $FD$, $XF$ and $DE$ meet at points $J$, $K$, $L$, respectively. Let further $M$, $N$, $P$ be points on the sides $BC$, $CA$, $AB$, respectively, such that the lines $AM$, $BN$, $CP$ be concurrent. Prove that the lines $JM$, $KN$ and $LP$ are concurrent.