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See attached. What is the length of the minor arc PQ

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See attached. What is the length of the minor arc PQ [#permalink] New post 29 Jan 2004, 04:54
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 [#permalink] New post 29 Jan 2004, 05:29
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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 [#permalink] New post 29 Jan 2004, 06:10
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] New post 20 May 2006, 18:10
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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arc.JPG [ 11.97 KiB | Viewed 1239 times ]


Last edited by pesquadero on 20 May 2006, 19:09, edited 1 time in total.
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Re: PS: Minro Arc [#permalink] New post 20 May 2006, 18:48
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] New post 20 May 2006, 19:08
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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 [#permalink] New post 20 May 2006, 20:19
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 = 180-70-70 = 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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 [#permalink] New post 21 May 2006, 13:56
(A) also

18*Pi*110/360 - 18*Pi*70/360 = 2Pi
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Circle Question [#permalink] New post 19 Apr 2008, 19:16
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] New post 19 Apr 2008, 20:00
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 re-draw the diagram or re-write the problem?
QR is not the diameter.
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Re: Circle Question [#permalink] New post 20 Apr 2008, 08:57
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] New post 20 Apr 2008, 10:47
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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 180-90-35 = 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] New post 16 May 2011, 21:20
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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 180-140 = 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   [#permalink] 16 May 2011, 21:20
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