What is the area of the above circle?

Question

Q2.jpg What is the area of the above circle? 1) Angle ABC = 90 deg B) CD = 12 Weekly Quant Quiz #4 Ques 6

saukrit · Answer

Extended CB will touch the circle on point E(let us assume). Now DE has to be the diameter of the Circle. To be able to find length of DE we must be able to find the length of BE first. Now let us see if Either of the statements help us in finding the length of BE(where E is the point where extended CB touches the other end of circle).

1)Angle ABC = 90 deg . This only gives the length of AC the hypotenuse of triangle ABC. Hence  NOT SUFFICIENT 
2) CD = 12 . This info does not help us in finding the length of BE. Hence this too is  NOT SUFFICIENT

Hence, the  answer must be E

u1983 · Answer

1) Angle ABC = 90 deg.... NS .... we only get AC=17... not the radius or dia
2) CD = 12 .... NS .... we only get AD=25... not the radius or dia

Ans E

GMATBusters · Answer

This Question can be easily explained using one of the basic property:
 A Unique Circle can be drawn using 3 non-collinear points. 
As we need the radius of the circle, we need to find the relative position of points wrt each other.
Let us suppose that point C (0,0)
 Statement 1:  Points C (0,0), A(15,8), D(0,-k) where k is length of CD
Since all points are not defined , circle is not defined.
 NOT SUFFICIENT 
 Statement 2:  Points C (0,0), D(0,-12), point A not defined.
 NOT SUFFICIENT

combining Statement 1& 2 , we get 
Points are A(15,8) C(0,0) and D(0, -12), hence a unique circle can be drawn and its area can be calculated.
 SUFFICIENT.   
  Answer C

(Since, It is a DS Question, there is no need to find the exact area, we need to know whether it can be determined uniquely or not)

What is the area of the above circle?

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