Question 6
In triangle $KLM$, the internal angle bisectors $KN$ and $LP$ intersect at $Q$, with $N$ on $LM$ and $P$ on $KM$. Point $M$ lies on the circle through $P,Q,N$. If $PN=2$, compute $PQ$.
Answer entry: use sqrt(...) for a square root, * for multiplication and / for division, without spaces. The checker recognizes only explicitly listed exact forms; following this syntax does not guarantee recognition of every equivalent expression. An unrecognized equivalent form requires manual checking and must not be treated as wrong or scored zero solely because it is unrecognized.
Answer entry: use sqrt(...) for a square root, * for multiplication and / for division, without spaces. The checker recognizes only explicitly listed exact forms; following this syntax does not guarantee recognition of every equivalent expression. An unrecognized equivalent form requires manual checking and must not be treated as wrong or scored zero solely because it is unrecognized.