How many locations for the lampposts are possible?

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Quandaries & Queries

Subject: Locus
Name: Madeeha
Who are you: Student

Maria's backyard has two trees that are 40 feet apart, as shown in the accompanying diagram. She wants
to place lampposts so that the posts are 30 feet from both of the trees. Draw a sketch to show where the
lampposts could be placed in relation to the trees. How many locations for the lampposts are possible?

Madeeha,

I can get you started.

Take a compass and set the distance between the metal point and the pencil point to be 3/4 of the distance between the trees in the diagram. In the scale of the diagram this is 30 feet. Put the metal point at the location of the first tree and draw a circle. If a lamppost is to be 30 feet from the first tree it must be on this circle.

Can you complete the problem now?
Penny

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