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

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

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15 Dec 2018, 10:15
1
4
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Difficulty:

75% (hard)

Question Stats:

44% (02:03) correct 56% (02:08) wrong based on 52 sessions

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GMATbuster's Weekly Quant Quiz#13 Ques #4

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

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Re: Point A lies on a circle whose center is at point C. Does point B lie  [#permalink]

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15 Dec 2018, 11:13
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.

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Re: Point A lies on a circle whose center is at point C. Does point B lie  [#permalink]

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15 Dec 2018, 22:04
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.
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Re: Point A lies on a circle whose center is at point C. Does point B lie  [#permalink]

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16 Dec 2018, 03:55
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

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Re: Point A lies on a circle whose center is at point C. Does point B lie  [#permalink]

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16 Dec 2018, 23:11
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.
Re: Point A lies on a circle whose center is at point C. Does point B lie   [#permalink] 16 Dec 2018, 23:11
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