You are planning a graduation party in the triangular courtyard shown. You want to fit as large a circular tent as possible on the site without extending into the walkway.

a. Copy the triangle and show how to place the tent so that it just touches each edge. Then explain how you can be sure that there is no place you could fit a larger tent on the site. Use sketches to support your answer. 

b. Suppose you want to fit as large a tent as possible while leaving at least one foot of space around the tent. Would you put the center of the tent in the same place as you did in part (a)? Justify your answer.

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