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.
Maximum distance between two points on a circle is the length of its diameter (so when these points are the endpoints of a diameter), so the max distance = diameter = 2 radii.
So for example if we are told that the distance between the two points on a circle is 10cm then we can be sure that the diameter is more than or equal to 10 (or the radius is more than or equal to 10/2=5).
Next, the formula to calculate the distance between two points
(x_1,y_1) and
(x_2,y_2) is
d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}.
Now, back to the original question:
Is the radius of the circle greater than 3?1) (2,4) and (5,10) lie on the circle --> the distance between these points is
d=\sqrt{(2-5)^2+(4-10)^2}=\sqrt{45}>6, so the diameter of this circle must be more than 6, thus the radius must be more than 3 --> answer to the question is YES. Sufficient.
2) (2,4) and (4,1) lie on the circle --> the distance between these points is
d=\sqrt{(2-4)^2+(4-1)^2}=\sqrt{13}<6, so the diameter of this circle may or may not be more than 6. Not sufficient.
Answer: A.
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41% (01:39) correct
