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# Did ETS make a mistake on this question?

This is the question: "Three circles with their centers on line segment PQ are tangent at points P, R, and Q, where point R lies on line segment PQ." Which is greater sum of two smaller circles circumferences or the larger circle circumference?

Your video explanation and ETS explain that the answer is C, assuming that line PQ is equivalent to the diameter, but I don't understand how that assumption can be made, which is why I chose D. Please explain what I overlooked. Thank you!

Author

Posted Jan 8, 2015

### 1 Explanation

1 Sam Kinsman, Magoosh Tutor

Hi there! Notice that the question says "three circles with their centers on line segment PQ," which tells us that PQ goes through the center of all three circles. We also know that the three circles "are tangent at points P, R, and Q," which tells us that the circles must cover the whole line, all the way from point P to Q. Therefore, PQ must be the diameter of the largest circle!

Nov 5, 2015 • Comment