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See attached. What is the length of the minor arc PQ [#permalink]
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29 Jan 2004, 05:54
See attached. What is the length of the minor arc PQ?
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Manager
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D) 9/2 phi, length of the arc= (theta/360) * 2 phi r, we get theta=90 and radius=9, so length of arc PQ= 9/2 phi



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The circumference is 18Pi. The arc PQ minor is 40┬░ which is 1/9 circumference. Then PQ=2Pi. I will go with A.)



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PS: Minro Arc [#permalink]
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20 May 2006, 19:10
In the circle shown, PQ is parallel to diameter OR, and OR has a length of 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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Last edited by pesquadero on 20 May 2006, 20:09, edited 1 time in total.



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Re: PS: Minro Arc [#permalink]
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20 May 2006, 19:48
pesquadero wrote: In the circle shown, PQQ is parallel to diameter OPand OR has a length of 18. What is the length of the minor arc PQ? a) 2pi b) 9pi/4 c) 7pi/2 d) 9pi/2 e) 3pi
make sure you posted the question correctly.



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Re: PS: Minro Arc [#permalink]
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20 May 2006, 20:08
Professor wrote: pesquadero wrote: In the circle shown, PQQ is parallel to diameter OPand OR has a length of 18. What is the length of the minor arc PQ? a) 2pi b) 9pi/4 c) 7pi/2 d) 9pi/2 e) 3pi make sure you posted the question correctly.
Sorry about that.. Question has been corrected.



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One thing to keep in mind in Arc question is whether the angle that is given is from either the center of the circle or from the edge of the circle (such as this example)
If angle is from the middle of the circle:
THE LENGTH OF ARC = (angle * pi * Radius)/180
If angle is not from the middle of circle: also known as MINOR ARC
(Minor arc always have twice the measure of the inscribed angle)
therefore in this case ARC OP = 2*X, since X = 35. OP=70
PQ  OR so PQ = 1807070 = 40
But remember that 40 in reference to the whole circle is 40/360 = 1/9 of the circumference
Circumference of circle= 2*pi*R = 18*pi
therefore PQ = (18*pi)/9 = 2*pi



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(A) also
18*Pi*110/360  18*Pi*70/360 = 2Pi



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Circle Question [#permalink]
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19 Apr 2008, 20:16
In the circle show, PQ is parallel to diameter QR. and QR has length 18. What is the length of the minor arc PQ? a. 2pie b. 9pie/4 c. 7 pie / 2 d. 9 pie / 2 e. 3 Pie
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Re: Circle Question [#permalink]
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19 Apr 2008, 21:00
dishant007 wrote: In the circle show, PQ is parallel to diameter QR. and QR has length 18. What is the length of the minor arc PQ?
a. 2pie b. 9pie/4 c. 7 pie / 2 d. 9 pie / 2 e. 3 Pie Can you redraw the diagram or rewrite the problem? QR is not the diameter.



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Re: Circle Question [#permalink]
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20 Apr 2008, 09:57
Quote: In the circle show, PQ is parallel to diameter QR. and QR has length 18. What is the length of the minor arc PQ?
a. 2pie b. 9pie/4 c. 7 pie / 2 d. 9 pie / 2 e. 3 Pie
In the circle show, PQ is parallel to diameter OR. and OR has length 18. What is the length of the minor arc PQ? a. 2pie b. 9pie/4 c. 7 pie / 2 d. 9 pie / 2 e. 3 Pie Sorry for the typo



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Re: Circle Question [#permalink]
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20 Apr 2008, 11:47
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A.
First, draw line PO to obtain triangle OPR. We know that a triangle inscribed a half circle with one side being the diameter of a circle is always a right triangle. This means angle OPR is a right angle. Given that angle PRO is 35, we know that angle POR is 1809035 = 55
Set center point of circle = C Since POR = POC = 55, this means OPC = 55, and PCO = 180  55  55 = 70. Using symmetry, we know that angle PCQ is 180  70  70 = 40
Therefore, Length of arc PQ = 40/360 * pi*18 = 2*pi



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Re: Circle Question [#permalink]
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16 May 2011, 22:20
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To find the length of minor arc PQ, we need to get the angle extended by the arc at the center of the circle. Name the center as C. We need to find the angle PCQ and substitute in the formula (θ/360)*2πr where θ is the angle subtended by the arc at the center. Step 1:
Since the lines OR and PQ are parallel and Angle ORP is 35 degrees, as per alternate angles rule, angle RPQ is 35 degrees.
Step 2:
Draw a line from P to C. Line PC is equal to CR, which is the radius i.e 9. Now consider the triangle RPC. In this triangle, 2 sides are equal PC and CR and the angle CRP is 35 degrees. As per the rules of isosceles triangle, angle RPC must also be 35 degrees.
So, the total angle CPQ is 70 degrees.
Step 3:
Draw a line from Q to C. So, line PC is equal to line QC. If angle CPQ is 70 degrees, then angle PQC will also be 70 degrees.
Finally, angle PCQ is 180140 = 40 degrees
Step 4:
Substitute 40 in the formula (θ/360)*2πr = (40/360)*(2*π*9) = 2π
The answer is (A)




Re: Circle Question
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