In the figure above, arc QRO is a semicircle. What is the area of the

Question

https://gmatclub.com/forum/download/file.php?id=28843 In the figure above, arc QRO is a semicircle. What is the area of the circle with center O? (1) The area of triangle PQO is 30. (2) The length of QRO is 2.5π. 2016-01-04_0044.png

BrainLab · Answer

(1) Area of triangle = 30, clearly not sufficient, we cannot enforce it to be 5:12:13 trianlge
(2) If the length is equal to 2.5π then the diameter of the small circle is equal to 5 (whole length = 5π and circumference=π*d, hence d=5) Not sufficient
(1) + (2) Now we know that the small side of a triangle = 5 and from the Area formula PO*QO=60 -> PO=60/5=12, so we have a 5:12:13 triangle, hence PO=Radius=13. It's sufficient to calculate the area of the big circle.
Answer C

paidlukkha · Answer

where does it say QRO is 1/2 of the big circle
just says QRO is a semicircle
so E!

oanhnguyen1116 · Answer

To calculate area of the circle with center O, we need to know the radius PO.
(1) => 1/2 *QO * PO = 30.
QO unknown => no way to know PO.

(2) => know QO. But how to know PO? No way

(1) + (2) => know QO => know PO => know area :-D

C is correct

C is correct

fskilnik · Answer

? = {S_{{	ext{big}}\,\, \odot }}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\boxed{\,? = OP\,}\,

https://i.ibb.co/tDn3WCn/10-Dec18-2h.gif

\left( {1 + 2} ight)\,\,\,\,\left\{ \matrix{
 \,\left( 2 ight)\,\,\, \Rightarrow \,\,\,OQ = 5 \hfill \cr 
 \,\left( 1 ight)\,\,\, \Rightarrow \,\,\,30 = {{OP \cdot OQ} \over 2} \hfill \cr} ight.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,?\,\, = \,\,\,OP\,\,{m{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {m{C}} ight)

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

In the figure above, arc QRO is a semicircle. What is the area of the

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In the figure above, arc QRO is a semicircle. What is the area of the

Prep Toolkit

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