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Computers are being used more and more to solve geometric problems, like modeling physical objects such as brains and bridges.
Given that \(P\) denotes a set of point, the pseudocode shown below checks if lines are collinear by checking if the point \(p\),\(q\), and \(r\) are collinear, where \(q\) is the central point, by checking if the the slopes of the segments \(\overline { pq }\) and \(\overline { qr }\) are identical.
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What is the worst case running time of the algorithm?
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The following text file contains a set of triplets. Each triplets contains three integers \(x,y,R\), representing a circle of radius \(R\) centered at \((x,y)\). Out of each pair of circles in the file, how may of them intersect?
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How many of the pairs of line segments in this text file intersect?
Details and assumption
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