The distance from school to the monument in the town centre is \(4.2\) km and the distance from Anna’s house to school is \(0.7\) km. Given that the distance from Anna’s house to the monument is an integer number of kilometres, what is this distance?
Tom and his grandma live on the same side of a straight river. Tom wants to visit his grandma, but also wants to stop by the river and fill his bottle with water. What is the shortest path that starts at his house, touches the river and ends at his grandma’s house?
Show that for any three points on the plane \(A,B\) and \(C\), \(AB \ge |BC - AC|\).