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Question on arc length

This topic has 1 expert reply and 0 member replies

Question on arc length

Post Sun Oct 23, 2016 9:50 pm
Would be grateful if you could help me with the following question. I understand that the arc length is the sector of a circle; in the answer, the circumference has been subtracted from the minor arc (central angle) to get the result. But would the central arc not be included on the big arc ABC? Why has that been subtracted?
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Post Mon Oct 24, 2016 10:15 am
Hi sucheta.lahiri,

If this is a GMAT question, then you should include the 5 answer choices. In many cases, the answers provide a clue as to how you might go about solving the problem (and potentially avoid most/all of the 'math').

This prompt can be approached in a couple of different ways. I'm going to walk you through how to add some lines to this picture so that you can use the implied angles to get to the correct answer. You can use a variation on TESTing VALUES to get to the solution.

1) To start, the prompt does NOT state if AB and AC are equal, so they clearly don't have to be. By extension, BC could be the diameter. Draw a new picture with that idea in mind.
2) Next, you can create triangle ABC. Since BC is the diameter, angle A must be 90 degrees. What does that make angle C?
3) Draw two radii out from the center to point A and point C. You now have an ISOSCELES triangle. Since you have angle C, you can fill in the other two angles.
4) With the central angle AOC = 80 degrees, you now know what Arc ABC is: 280 degrees. You can now calculate the arc length.

Final Answer: (280/360)(36pi) = 28pi

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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