1984 AIME Problem 6

Three circles, each of radius 3, are drawn with centers at (14, 92), (17, 76), and (19, 84). A line passing through (17,76) is such that the total area of the parts of the three circles to one side of the line is equal to the total area of the parts of the three circles to the other side of it. What is the absolute value of the slope of this line?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.