We're looking for a treasure Here's a problem my sister-in-law just sent me and she doesn't find the answer. It's to help her daughter.
We have a map of an island. On this island there's a palm tree P, a house M and a big rock R. The rock is 8 meters far from the palm tree, and 5 meters far from the house. The house is 4 meters far from the palm tree. And we know that:


*

*the treasure  is < 6 meters from the palm tree

*the treasure  is > 4 meters from the house

*the treasure  is < 5 meters from the rock


On the island below put points M and P using the previous clues.
Color the zone where we have to dig to be sure to find the treasure.

Could you explain the basic principles of how to solve that problem/draw what's asked (the picture is not the actual one)?

First of all, to place the palm tree, house and big rock, we notice that any three points form a triangle or a line in the plane. Let's assume it is a triangle, with side lengths as given: 8, 5 and 4 meters respectively. Draw a triangle with these measurements (in centimeters).
The second step is to look at the distances of the treasure from the objects. In general, when an object is $<x$ meters from a point, it is within a circle of radius $x$ meters. So draw a circle of radius $6$ around the palm tree, an circle of radius $5$ around the rock and a circle of radius $4$ around the house. Your treasure is in the intersection of the two first circles, but outside the third circle.
