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What is the area of the above circle?

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What is the area of the above circle? [#permalink] New post   13 Oct 2018, 10:25
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A
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C
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E

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75% (hard)

Question Stats:

40% (02:09) correct 60% (02:06) wrong based on 49 sessions
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What is the area of the above circle?
1) Angle ABC = 90 deg
B) CD = 12

Weekly Quant Quiz #4 Ques 6

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C
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Re: What is the area of the above circle? [#permalink] New post   13 Oct 2018, 21:09
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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)
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Re: What is the area of the above circle? [#permalink] New post   13 Oct 2018, 10:43
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
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Re: What is the area of the above circle? [#permalink] New post   13 Oct 2018, 11:04
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
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Re: What is the area of the above circle? [#permalink]
13 Oct 2018, 11:04
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Bunuel
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