The triangle [[$ ABC $]] is equilateral. Draw a picture of the triangle when the sides are [[$ 4 $]] cm long. Determine the area where the point [[$ P $]] is located. [[$ P $]] fulfills the following conditions.

(1.) [[$ P $]] is closer to side [[$ AB $]] than side [[$ BC $]].
(2.) [[$ P $]] is less than [[$ 3 $]] cm from the vertex [[$ A $]].
(3.) [[$ P $]] is no more than [[$ 2 $]] cm from the side [[$ BC $]].

Take a picture of your solution and return it to the submission folder.

Solution