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# In the circle below, PQ is parallel to diameter OR and OR

Author Message
VP
Joined: 02 Jun 2006
Posts: 1202
In the circle below, PQ is parallel to diameter OR and OR  [#permalink]

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07 Aug 2006, 08:49
2
00:00

Difficulty:

(N/A)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 13 sessions

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In the circle below, PQ is parallel to diameter OR and OR has length 18. What is the length of the minor arc PQ?

A. 2pi
B. 9pi/4
C. 7pi/2
D. 9pi/2
E. 3pi

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Manager
Joined: 04 May 2006
Posts: 165
Location: paris

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07 Aug 2006, 10:52
oops

If the angle is 35 , the arc should be pi-2*(70) = 2*pi/9 ?
Manager
Joined: 02 Apr 2006
Posts: 152

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07 Aug 2006, 11:34
haas_mba07 wrote:
In the circle below, PQ is parallel to diameter OR and OR has length 18. What is the length of the minor arc PQ?

A. 2pi
B. 9pi/4
C. 7pi/2
D. 9pi/2
E. 3pi

I think its A...2 Pi

lenghth of arc PQ = circumference of the semicircle - (length of arc OP+Length of arc QR)

Circum ference = 2pir/2 = 9pi
arc OP= 35/360 (2pi18) since lines are parallel angle ORP = angle ROQ
arc QR= 35/360 (2pi18) (we should use the diameter as the radius here to find the lengths of the arcs)
hence length of arc PQ= 9pi- 2(35pi/10) = 2pi
Manager
Joined: 26 Jun 2006
Posts: 151

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07 Aug 2006, 11:57
(A) 2pi

I first assumed that 35 refers to the length of PR (because it did not have the degree sign after) and this sent me on the wrong track initially, but ten I quickly realized that 35 is a measurement of an angle...

Anyway...

PO=OR, so <OPR=35". From here, <POE=180-35*2=110

Let's call <OPQ=x. Then, since OP=OQ, <PQO=x

From triangle OPQ, <POQ=180-2x.

Since PQ||OR, <QOR=<PQO=x

So, <POR=<POQ+<QOR=(180-2x)+x=180-x

But, from the first line we know that <POR=110

So, 180-x=110 => x=70.

Finally, <POQ=180-70*2=40 and the length of the arc PQ equal

(40/360)*(2*pi*9) = 2*pi
VP
Joined: 02 Jun 2006
Posts: 1202

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07 Aug 2006, 12:35
Thanks guys!

OA is A. 2pi

Official Guide 11Ed problem;
Problem solving : pg 180, Prob# 206
SVP
Joined: 30 Mar 2006
Posts: 1661

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08 Aug 2006, 02:25
1
A 2Pi.

Arc OP = 2* 35 = 70
Arc QR = 2*35 = 70
Arc OR = 180
=> Arc OP + ArcPQ + ArcQR = 180
=> ArcPQ = 40

PQ = 40/360 * 2Pi * 9
= 2Pi
Non-Human User
Joined: 09 Sep 2013
Posts: 9457
Re: In the circle below, PQ is parallel to diameter OR and OR  [#permalink]

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13 Jan 2019, 00:52
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Re: In the circle below, PQ is parallel to diameter OR and OR &nbs [#permalink] 13 Jan 2019, 00:52
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