Write a clear set of steps for the construction of an equilateral triangle. Use Euclid’s Proposition 1 as a guide.

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suppose two circles are constructed using the following instructions:

Draw circle: center A, radius

Draw circle: center C, radius

Under what conditions (in terms of AB, CD, AC) do the circles have one point in common?

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Under what conditions (in terms of AB, CD, AC) do the circles have no points in common?

Under what conditions (in terms of AB, CD, AC) do the circles have two points in common?

Under what conditions (in terms of AB, CD, AC) do the circles have more than two points in common? Why?

You need a compass and a straightedge.

Cedar City boasts two city parks and is in the process of designing a third. The planning committee would like all three parks to be equidistant from one another to better serve the community. A sketch of the city appears below, with the centers of the existing parks labeled as P_{1} and P_{2}. Identify two possible locations for the third park and label them as P_{3a} and P_{3b} on the map. Clearly and precisely list the mathematical steps used to determine each of the two potential locations.

Answer all parts of the problem below.

Draw your sketch on paper, take a picture, and upload it using the image upload icon:

If you do not have the ability to upload an image of your work type "Sketch is on paper."

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