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If P, Q and R are the centers of circles P, Q, and R and the
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22 Jul 2014, 07:34
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If P, Q and R are the centers of circles P, Q, and R and the points P, Q, R and T all lie on the same line, what portion of circle P is shaded? A. 3/16 B. 1/5 C. 6/25 D. 1/4 E. 3/8 Hi, I want to know why we don't get same answer using PQ = 2? OE Let us say that line segment RT has a length of 1. RT is the radius of circle R, so circle R has a radius of 1. Line segment QT is the diameter of circle R, so it has a length of 2 (twice the radius of circle R). Segment QT also happens to be the radius of circle Q, which therefore has a radius of 2. Line segment PT, being the diameter of circle Q, has a length of 4. Segment PT also happens to be the radius of circle P, which therefore has a radius of 4. The question is asking us what fraction of circle P is shaded. The answer will be (shaded area) ÷ (area of circle P) The area of circle P is π(4)2, which equals 16π. The shaded area is just the area of circle Q (i.e. π(2)^2, which equals 4π) minus the area of circle R (i.e. π(1)^2, which equals π). Therefore, the answer to our question is (4π  π) / 16π Attachment:
Eye of the Tiger.jpg [ 11.43 KiB  Viewed 13480 times ]
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If P, Q and R are the centers of circles P, Q, and R and the
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22 Jul 2014, 07:51
goodyear2013 wrote: If P, Q and R are the centers of circles P, Q, and R and the points P, Q, R and T all lie on the same line, what portion of circle P is shaded? A. 3/16 B. 1/5 C. 6/25 D. 1/4 E. 3/8 Hi, I want to know why we don't get same answer using PR = 2? OE Let us say that line segment RT has a length of 1. RT is the radius of circle R, so circle R has a radius of 1. Line segment QT is the diameter of circle R, so it has a length of 2 (twice the radius of circle R). Segment QT also happens to be the radius of circle Q, which therefore has a radius of 2. Line segment PT, being the diameter of circle Q, has a length of 4. Segment PT also happens to be the radius of circle P, which therefore has a radius of 4. The question is asking us what fraction of circle P is shaded. The answer will be (shaded area) ÷ (area of circle P) The area of circle P is π(4)2, which equals 16π. The shaded area is just the area of circle Q (i.e. π(2)^2, which equals 4π) minus the area of circle R (i.e. π(1)^2, which equals π). Therefore, the answer to our question is (4π  π) / 16π The radius of P is twice the radius of Q, which is twice the radius of R. Say the radius of R is 1, so the radius of Q is 2 and the radius of P is 4. The area of the shaded region = area of Q  area of R = \(4\pi\pi=3\pi\). The area of P = \(16\pi\). The ratio = 3/16. Answer: A. As for your question PR is not the radius of any circle, so assuming a value for it is not a good idea. PR = radius of Q + radius of R = 2x + x = 2 > radius of R = x = 2/3 > the radius of Q is 4/3 > the radius of P is 8/3. The area of the shaded region = area of Q  area of R = \(\frac{16}{9}\pi\frac{4}{9}\pi=\frac{12}{9}\pi\). The area of P = \(\frac{64}{9}\pi\). The ratio = 12/64 = 3/16. Thew same answer.
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Re: If P, Q and R are the centers of circles P, Q, and R and the
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22 Jul 2014, 08:09
goodyear2013 wrote: Hi, I want to know why we don't get same answer using PQ = 2?
PQ is the radius of the middle circle, Q. In my solution above I assumed exactly that PQ = QT = 2.
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Re: If P, Q and R are the centers of circles P, Q, and R and the
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03 Jul 2016, 05:25
goodyear2013 wrote: Attachment: Eye of the Tiger.jpg If P, Q and R are the centers of circles P, Q, and R and the points P, Q, R and T all lie on the same line, what portion of circle P is shaded? A. 3/16 B. 1/5 C. 6/25 D. 1/4 E. 3/8 Hi, I want to know why we don't get same answer using PQ = 2? OE Let us say that line segment RT has a length of 1. RT is the radius of circle R, so circle R has a radius of 1. Line segment QT is the diameter of circle R, so it has a length of 2 (twice the radius of circle R). Segment QT also happens to be the radius of circle Q, which therefore has a radius of 2. Line segment PT, being the diameter of circle Q, has a length of 4. Segment PT also happens to be the radius of circle P, which therefore has a radius of 4. The question is asking us what fraction of circle P is shaded. The answer will be (shaded area) ÷ (area of circle P) The area of circle P is π(4)2, which equals 16π. The shaded area is just the area of circle Q (i.e. π(2)^2, which equals 4π) minus the area of circle R (i.e. π(1)^2, which equals π). Therefore, the answer to our question is (4π  π) / 16π Shaded region = area of circle Qarea of circle R =pi*(QT)^2pi*(RT)^2 but QT=2RT pi*(QT^2QT^2/4)>pi*3/4QT^2 but again PT=2QT substituting>3/4*pi*(PT/2)^2 3/16*pi*PT^2>3/16*area of circle P Ans A



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Re: If P, Q and R are the centers of circles P, Q, and R and the
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01 Jun 2017, 16:57
goodyear2013 wrote: Attachment: Eye of the Tiger.jpg If P, Q and R are the centers of circles P, Q, and R and the points P, Q, R and T all lie on the same line, what portion of circle P is shaded? A. 3/16 B. 1/5 C. 6/25 D. 1/4 E. 3/8 Hi, I want to know why we don't get same answer using PQ = 2? OE Let us say that line segment RT has a length of 1. RT is the radius of circle R, so circle R has a radius of 1. Line segment QT is the diameter of circle R, so it has a length of 2 (twice the radius of circle R). Segment QT also happens to be the radius of circle Q, which therefore has a radius of 2. Line segment PT, being the diameter of circle Q, has a length of 4. Segment PT also happens to be the radius of circle P, which therefore has a radius of 4. The question is asking us what fraction of circle P is shaded. The answer will be (shaded area) ÷ (area of circle P) The area of circle P is π(4)2, which equals 16π. The shaded area is just the area of circle Q (i.e. π(2)^2, which equals 4π) minus the area of circle R (i.e. π(1)^2, which equals π). Therefore, the answer to our question is (4π  π) / 16π Bunuel why can't RT be 1/2? The largest square in this diagram is P, the second biggest, Q and the smallest R  so if the radius of r is 1/2 then the radius of Q is 1 and the radius of P is 2 but I don't understand why I can't get 3/8 using this method.



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Re: If P, Q and R are the centers of circles P, Q, and R and the
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01 Jun 2017, 20:52
Nunuboy1994 wrote: Bunuel why can't RT be 1/2? The largest square in this diagram is P, the second biggest, Q and the smallest R  so if the radius of r is 1/2 then the radius of Q is 1 and the radius of P is 2 but I don't understand why I can't get 3/8 using this method. You can do that way too. This is a ratio question so if you do math correctly you should get the same answer no matter what numbers you use. But how can I tell what you did incorrectly if you don't show your work?
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Re: If P, Q and R are the centers of circles P, Q, and R and the
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05 Jun 2017, 10:49
We know, QT = 2 RT and PT = 2 QT or PT = 4 RT.
Let RT = 1. So, QT = 2 and PT = 4
Now, area of circle P, Q and R will be 16π, 4π and π respectively.
From this we get that area of circle R is 1/4 area of circle Q and 1/16 of circle P. Also, area of circle Q is 1/4 area of circle P.
So area of shaded region = area of circle P  area of circle Q + area of circle R = 16π  4π + π = 13π
Therefore, the portion of circle P which is shaded = (16π  13π)/16π = 3/16.



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Let the circle with center P radius be x. Area PPi*(x2) Then radius of circle with center Q is x/2. Area QPi(x2/4) With same method area of circle RPi*(x2/16) Area of shaded region Pi (x2/4x2/16)= Pi *(3x2/16)
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Re: If P, Q and R are the centers of circles P, Q, and R and the
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05 Jun 2017, 23:55
goodyear2013 wrote: If P, Q and R are the centers of circles P, Q, and R and the points P, Q, R and T all lie on the same line, what portion of circle P is shaded? A. 3/16 B. 1/5 C. 6/25 D. 1/4 E. 3/8 Hi, I want to know why we don't get same answer using PQ = 2? OE Let us say that line segment RT has a length of 1. RT is the radius of circle R, so circle R has a radius of 1. Line segment QT is the diameter of circle R, so it has a length of 2 (twice the radius of circle R). Segment QT also happens to be the radius of circle Q, which therefore has a radius of 2. Line segment PT, being the diameter of circle Q, has a length of 4. Segment PT also happens to be the radius of circle P, which therefore has a radius of 4. The question is asking us what fraction of circle P is shaded. The answer will be (shaded area) ÷ (area of circle P) The area of circle P is π(4)2, which equals 16π. The shaded area is just the area of circle Q (i.e. π(2)^2, which equals 4π) minus the area of circle R (i.e. π(1)^2, which equals π). Therefore, the answer to our question is (4π  π) / 16π Attachment: Eye of the Tiger.jpg Let the radius of circle R = 1 unit So Radius of circle Q = 2 unit Radius of circle P = 4 unit Area of shaded region : pi(2^2)  pi(1^1) = 3pi Area of circle P = pi(4^2 )= 16pi So ratio of shaded region to Circle P = 3pi/16pi = 3/16
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Re: If P, Q and R are the centers of circles P, Q, and R and the
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06 May 2019, 20:11
goodyear2013 wrote: If P, Q and R are the centers of circles P, Q, and R and the points P, Q, R and T all lie on the same line, what portion of circle P is shaded? A. 3/16 B. 1/5 C. 6/25 D. 1/4 E. 3/8 We can let the radius of circles P, Q, and R be 4, 2, and 1, respectively. Therefore, the area of circle P is π(4)^2 = 16π, that of circle Q is π(2)^2 = 4π, and that of circle R is π(1)^2 = π, The area of the shaded region is the difference between the areas of circle Q and circle R. Therefore the area of the shaded region is 4π  π = 3π, and hence 3π/(16π) = 3/16 of circle P is shaded. Answer: A
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Re: If P, Q and R are the centers of circles P, Q, and R and the
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