gdk800 wrote:
Hi All,
Please help me understand the following problem.
Question: Is the radius of the circle greater than 3?
1) (2,4) and (5,10) lie on the circle.
2) (2,4) and (4,1) lie on the circle.
My understanding is that the question asks us whether the radius of the circle greater than 3 or not? Thus if we are able to get a Yes or No from the option, it should suffice.
Yes. Your understanding is correct.
Now to solve this problem, observe the fact that for any two points on circle, the greatest distance possible between them is equal to the diameter of the circle. Now, through two points infinite number of circles may be drawn. But the fact we just observed tells us that the smallest such circle will have the diameter equals to the distance between the points.
Statement 1: (2, 4) and (5, 10) lie on the circle.
Minimum possible diameter of the circle = Distance between (2, 4) and (5, 10)
= √[(5 - 2)² + (10 - 4)²]
= √[3² + 6²]
Clearly the minimum diameter is greater than 6.
Thus radius is always greater than 3.
Sufficient.
Statement 1: (2, 4) and (4, 1) lie on the circle.
Minimum possible diameter of the circle = Distance between (2, 4) and (4, 1)
= √[(4 - 2)² + (1 - 4)²]
= √[2² + 3²]
= √13
As √13 < 6, the minimum diameter is less than 6.
Thus radius is may or may not be greater than 3.
Not sufficient.
The correct answer is A.
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Firstly, thanks Rahul for posting the answer i was trying to get to because the following explains the reason i put this post for.
As √13 < 6, the minimum diameter is less than 6.
Thus radius is may or may not be greater than 3.
As √13 < 6, the minimum diameter is less than 6.
this means the radius is also less than 3 coz if Diameter < 6 than Diameter/2 (= Radius ) < 6/2 and thus it answers our question that the radius is NOT greater than 3. This is the reason i marked D and not A, which is the OA....
Kindly clarify, I will be much thankful
