Problem

Source: Czech-Polish-Slovak Junior Match 2012, Team p4 CPSJ

Tags: geometry, rhombus, Segment



A rhombus $ABCD$ is given with $\angle BAD = 60^o$ . Point $P$ lies inside the rhombus such that $BP = 1$, $DP = 2$, $CP = 3$. Determine the length of the segment $AP$.