gmatclubmember wrote:In the circle below PQ is parallel to diameter OR and OR has length 18. What is the length of minor arc PQ?
2PI
9PI/4
7PI/2
9PI/2
3PI
Arc lengths are always measured as a fraction of the cirumference. so in order to fid the arc length, we need two things:
1) The circumference: Since OR=18, the circumference is 18pi.
2) The fraction of the circumeference defined by the arc. This is determined by the arc's central angle out of 360. For example, an arc defined by a 90 degree cebtral angle will equal a quarter of the circumeference: 90 out of 360 is 90/360=1/4, so the arc is also 1/4 of the circum.
We don't know the central angle for arc PQ, but we can fid the central angles for arcs PO and QR, and subrtact those from 180 for the entire arc OR.
PRO is an inscribed angle of 35, so the corresponding central angle will be twice that, or 70.
Likewise, QOR will also equal 35 (inscribed angle), so the central angle will also be 70. Leaving a central angle of 180-70-70=180-140=40 angles for arc PQ, and a circumference fraction of 40/360=1/9.
So the final result is 1/9*18pi = 2pi. Answer is
A.
