In the figure above, acr QRO is a semicircle. What is the area of the circle with center O?
1) The area of the triangle PQO is 30.
2) The length of QRO is 2.5Ï€.
OA C.
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In the figure above, acr QRO is a semicircle. What is the
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In the figure above, acr QRO is a semicircle. What is the area of the circle with center O?
1) The area of the triangle PQO is 30.
2) The length of QRO is 2.5Ï€.
OA C.
In the figure above, acr QRO is a semicircle. What is the area of the circle with center O?
1) The area of the triangle PQO is 30.
2) The length of QRO is 2.5Ï€.
OA C.
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Jay@ManhattanReview
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We have to get the area of the circle with center O.AAPL wrote:Princeton Review
In the figure above, acr QRO is a semicircle. What is the area of the circle with center O?
1) The area of the triangle PQO is 30.
2) The length of QRO is 2.5Ï€.
OA C.
Let's take each statement one by one.
1) The area of the triangle PQO is 30.
1/2 * OP * OQ = 30 => R*2r = 60 => R*r = 30, wether OP = R = radius of the bigger circle and r = radius of the smaller circle
We know that the area of the bigger circle = πR^2, but we can't get the unique value of R. Insufficient.
2) The length of QRO is 2.5Ï€.
=> 2Ï€r/2 = 2.5Ï€ => r = 2.5. We can't get the unique value of R. Insufficient.
(1) and (2) together
From (1), we have R*r = 30 and from (2), we have r = 2.5, thus, R = 30/2.5 = 12.
Thus, the area of the bigger circle = πR^2 = π*(12)^2 = 144π. Sufficient.
The correct answer: C
Hope this helps!
-Jay
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Last edited by Jay@ManhattanReview on Tue Jan 15, 2019 8:41 pm, edited 1 time in total.
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fskilnik@GMATH
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$$? = {S_{{\text{big}}\,\, \odot }}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\boxed{\,? = OP\,}\,$$AAPL wrote:Princeton Review
In the figure above, arc QRO is a semicircle. What is the area of the circle with center O?
1) The area of the triangle PQO is 30.
2) The length of QRO is 2.5Ï€.
$$\left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{
\,\left( 2 \right)\,\,\, \Rightarrow \,\,\,OQ = 5 \hfill \cr
\,\left( 1 \right)\,\,\, \Rightarrow \,\,\,30 = {{OP \cdot OQ} \over 2} \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,?\,\, = \,\,\,OP\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\rm{C}} \right)$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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