If PR is the diameter, what is the length of QP in the circle shown ab

Question

https://gmatclub.com/forum/download/file.php?id=43658 If PR is the diameter, what is the length of QP in the circle shown above? (1) b = 2 (2) PQR is a right angle image003.jpg

GMATinsight · Answer

Here we see three right angle triangles and all are similar triangles

Due to similarity ratio,  1/a = b/1

i.e.  ab = 1 
 
   Question : Length of QP = ?  
 To answer this question we only need the either a or b so that we can calculate hypotenuse of right triangle with hypotenuse PQ

Statement 1 : b = 2

SUFFICIENT

Statement 2 : PQR is a right angle

We already know this hence this is redundant information

NORT SUFFICIENT

Answer: option A

ShankSouljaBoi · Answer

Hi @GAMTinsight How did you get to ab = 1. Can you please explain the similarity ratio used a bit more ???

Thanks

GMATinsight · Answer

It came using similar triangle property as attached here.

ShankSouljaBoi · Answer

Thank you so much. This is exactly what I needed

soapbolt · Answer

https://gmatclub.com/forum/if-arc-pqr-a ... 44057.html Bunnel and other experts posted great detailed solution for similar problem in the above link. Hope it helps

T-bezz · Answer

You can also approach it algebraically.

c^2= hypotenuse big triangle
 d^2= hypotenuse small triangle

a^2+1= c^2 
  b^2+1= d^2 
Substitution   c^2+d^2= 〖(a+b)〗^2 
Expansion of the quadratic  a^2+1+b^2+1=a^2+2ab+b^2 
Simplification  2=2ab -----> 1=ab

I hope this helps

If PR is the diameter, what is the length of QP in the circle shown ab

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