Problem Solving

vinviper1 wrote:In the circle above, the PQ is paralle to diamet OR and OR has length of 18. What is the length of minor arc PQ?

2Pi
9/4Pi
7/2Pi
9/2Pi
3Pi



With no diagram its tough(feel free to reference book), but they go on with a doubleing of the angle to ge tthe proprtion of the arc? Is this diferent than that angle/360 = that proportion of the circumference? Thanks!2Pi

hi -

there are two different types of angles associated with circles on the gmat.

one is the central angle; this is the one you're thinking of. its vertex is located at the center of the circle, so that its sides are like the hands on a clock. this kind of angle has a # of degrees that's equal to the # of degrees in the corresponding arc.

however, the other type of angle is the inscribed angle. this is an angle whose vertex is ON the circle. for this type of angle, the arc has twice the number of degrees of the angle. the angles in the problem you've cited are inscribed angles, so, if the angles have 35 degrees apiece, the arcs have 70 degrees apiece.

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if you don't get the difference, try the following exercise:

* draw a central angle of 90 degrees. this should be really easy to do; it's just like drawing clock hands showing 3:00.
notice that the angle formed by the clock hands is also 90 degrees.

* draw an inscribed angle of 90 degrees; i.e., draw a right angle whose vertex is located ON the circle.
if you've drawn a decent diagram (circles are harder to draw than you might think), then you should notice that your right angle cuts off a semicircle (180 = twice 90).