Point A lies on a circle whose center is at point C. Does point B lie

Question

GMATbuster's Weekly Quant Quiz#13 Ques #4 
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Point A lies on a circle whose center is at point C. Does point B lie inside the circle?
1. BC^2 = AC^2 + AB^2
2. ∠CAB is greater than ∠ABC

rajatvermaenator · Answer

1)BC is hypotenuse of a right triangle ABC. where AC is radius. So angle will be right angle since opposite to BC. The only possible way it can happen is if B lies on a tangent to point A. Hence B lies out of the circle. Sufficient.
2) suppose B is on the circle , then A and B both will be radius , the triangle ABC will be isosceles triangle. With angle A and B equal.for angle A to be bigger you have to increase BC, so b has to lie outside circle. Sufficient. 
Answer is D

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Ritwick91 · Answer

Option-1:
BC^2=AB^2+AC^2
=> A is right angle
=> BA is perpendicular to CA
And that is only possible if BA is a tangent to the circle (A is on circle and CA is the radius)
So, we can conclude that B lies outside circle (to be a tangent)

Option-2:
The given condition doesn't say anything about exact value of the angles and hence cannot be used to decide if B lies outside/inside the circle.

Hence, IMO ans is A.

shashankism · Answer

Given : Point A lies on a circle whose center is at point C.

DI Question : Does point B lie inside the circle?

Statement 1. BC^2 = AC^2 + AB^2 
-> BC>AC
Since A lies on on circle. That means BC is greater than radius. 
Position B3 represent the same in the figure where BC^2 = AC^2 + AB^2 i.e. AB is a tangent to the circle and ∠BAC = 90. So, B must lie on the tangent to the circle and hence will always lie outside or on the circle but not inside the circle.
  SUFFICIENT

Statement 2. ∠CAB is greater than ∠ABC 
Lets consider Position B2 i.e. Point B lies on the circle where ∠CAB = ∠ABC. 
Now when we bring point B at position B1 i.e inside circle ∠CAB < ∠ABC. 
If we bring point B at position B4 i.e outside circle ∠CAB > ∠ABC. 
  SUFFICIENT

Answer D

ritu1009 · Answer

Statement 1 is sufficient
since point A lies on the circle and AB is perpendicular to Ac , hence AB can only be tangent to the circle.
B lies outside the circle.

Statement 2
ínsufficient.

ChuHoaiNam2505 · Answer

What if A = B, i means that A and B are exactly 1 point so that AB=0 and AC=BC. In this case, whether B is still considered inside the Circle? If so, B is the correct answer

GMATBusters · Answer

If A = B, St 2 is invalid.
Hence A cannot be equal to B.

ChuHoaiNam2505 · Answer

Sorry but i dont really get your point.

In my opinion, From Statement 1, we cannot conclude that B lies outside the Circle because, if A=B, B still lies on a circle, right? So i think Statement 1 is insufficient. Can you help?

From statement 2, clearly B lies outside the Circle.

GMATBusters · Answer

you asked for the condition when A= B:

Statement 2: ∠CAB is greater than ∠ABC : 
this will not satisfy when A= B

ChuHoaiNam2505 · Answer

Ok, pls ignore the Statement 2, i know the Statement 2 is sufficient

What i am asking is about Statement 1.

If A can = B, is the statement 1 sufficient?
Because, if A = B, then B lies on the circle and ,in my opinion, it means that B lies inside the Circle. So my question becomes whether laying on the circle is counted as laying outside the circle?

GMATBusters · Answer

All these 3 are different scenarios: lie on the circle.= point C lie outside the circle.= point A lie inside the circle.= point B https://gmatclub.com/forum/download/file.php?id=54658 c.JPG

GMATBusters · Answer

if A = B, then B lies on the circle and not inside, and hence the answer to question prompt is NO.
But this assumption: A = B, is not sufficient to prove that Statement 1 is sufficient as we are not sure that A = B.

Rickooreo · Answer

In this question 34 number which is there, it can also contain students who have selected German right? similarly 27 in french and 49 can also contain those who have taken all the three classes

Point A lies on a circle whose center is at point C. Does point B lie

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