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

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

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.

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

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

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.

you asked for the condition when A= B:

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

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?

All these 3 are different scenarios:

• lie on the circle.= point C
  
• lie outside the circle.= point A
  
• lie inside the circle.= point B

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.

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