In the diagram above, S is the center of the circle. If QS = 5 and QR

Question

c4_img14.png In the diagram above, S is the center of the circle. If QS = 5 and QR = 6, what is PQ? A. 7 B. 8 C. 9 D. 10 E. 11 Kudos for a correct solution .

smit29may · Answer

Since PR is the diameter, 
PR=2*QS= 10.

Also, it's a given that if the diameter of a circle is one of the sides of a triangle, that triangle is a right angled triangle. Thus, we have PR as the hypotenuse and the other two sides as the legs at 90-angle. This makes the triangle a 
6-8-10 triangle.

So tha side we are looking for is 8.

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chetan2u · Answer

hi  Bunuel ,
i think question is incomplete...
it is given that S is the center but it does not make PR as diameter, since it is not mentioned anywhere that PR is a straight line.....
also if PR is not a straight line ,there can be various possible lengths of PQ...

Bunuel · Answer

Check the red part below:

OG13, page 272:
A figure accompanying  a data sufficiency problem  will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2). 
  Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.   
 You may assume that the positions of points, angles, regions, and so forth exist in the order shown  and that angle measures are greater than zero degrees. 
All figures lie in a plane unless otherwise indicated.

OG13, page 150:
 Figures:  A figure accompanying  a problem solving question  is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible. Exceptions will be clearly noted.  Lines shown as straight are straight , and lines that appear jagged are also straight.  The positions of points, angles, regions, etc., exist in the order shown , and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Hope it helps.

sharmaam · Answer

1>>
Since PR is the diameter of the circle ,the angle inscribed by the diameter will be a right angle.
Thus Angle PQR=90 deg
One can recognize a pytha-triplet 10,6,8 (Since PR=5+5)
So length of PQ=8

2>>
We can also solve this by denoting ang PQS and QPS as x 
and ang QRS and RQS as y
Then 2x+2y=180
therefore x+y=90 
Now x+y= Ang PQR=90 
Thus using the pythrag-triplets
PQ=8

chetan2u · Answer

hi ,
the problem is there are two lines PS and SR.... i agree these are two straight lines but combined are these one straight line..
it is a request if u have come across such a scenario in OG, pl share such a question.

Bunuel · Answer

PR seems straight so it IS straight. No need to over-complicate things...

vasili · Answer

Triangle PQR is right, with angle PQR=90 degrees

Since QS is a radius, we can assume from picture that SR is a radius as well, and PR is a diameter= 10

We can use "magic" ratios of sides of the right triangle: 3:4:5 to find QP

Answer B

mvictor · Answer

we have a 3-4-5 triplet x2
thus PQ = 8, answ. choice B.

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

First of all, QS is a radius, so if QS = 5, that means PS = SR = 5 and the diameter PR = 10. Furthermore, because PR is a diameter, that means triangle PQR is a right triangle, with ∠PQR = 90°. We know two sides of this right triangle: QR = 6, and PR = 10, so we can use the  Pythagorean Theorem  to find the third side.
(PQ)^2 + (QR)^2 = (PQ)^2
(PQ)^2 + (6)^2 = (10)^2
(PQ)^2 + 36 = 100
(PQ)^2 = 100 – 36 = 64
PQ = sqrt{64} = 8

Answer = B

bumpbot · Answer

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In the diagram above, S is the center of the circle. If QS = 5 and QR

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In the diagram above, S is the center of the circle. If QS = 5 and QR

Prep Toolkit

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