Question 7
a. $B$ and $C$ are on the segment $AD$ with $AB = CD$. Prove that for any point $P$ in the plane: $PA + PD \geq PB + PC$.
b. Given four points $A$, $B$, $C$, $D$ on the plane such that for any point $P$ on the plane we have $PA + PD \geq PB + PC$. Prove that $B$ and $C$ are on the segment $AD$ with $AB = CD$.
b. Given four points $A$, $B$, $C$, $D$ on the plane such that for any point $P$ on the plane we have $PA + PD \geq PB + PC$. Prove that $B$ and $C$ are on the segment $AD$ with $AB = CD$.