<Qua-2025-765>, hint
Let E be the midpoint of BC, then DE pass through N , then PN=CN <DNC=90
Hence DP=DC. Lets calculate the length of AN
A(0,2) c(2,0), N(6/5, 2/5) then AN=AD=2. AQ pass through the midpoint F of DN
and <AFD=<MND=90, hence QF//PN Hence QN//CD, QN=1/2 (CD)
