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Geometry - Máximum Radius

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Geometry - Máximum Radius [#permalink] New post 14 Jan 2014, 21:30
What si the maximum radius of a circle that passes through point a (4,0) and (-4,0)?

A) 8
B) 4
C) 8(2)^1/2
D) 4(2)^1/2
E) none of the above

Can someone help me?
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Re: Geometry - Máximum Radius [#permalink] New post 15 Jan 2014, 01:37
The biggest circle is a straight line with infinite radius.

Lets consider the straight line to pass through (-4, 0) and (4, 0). Largest radius = infinity and mini radius = 4.

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Re: Geometry - Máximum Radius [#permalink] New post 20 Jan 2014, 11:32
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To answer this question, you need to visualize these two points.

(4,0) and (-4,0)

Now, the X coordinate goes first (x, y). So you know you're going 4 units to the right of the center point. Then 4 units to the left of the center point. These two points lie on same horizontal axis (where y value is 0).

So if 1 point of a circle is on y=0 but 4 units to the right...the only other point of a circle that has y coordinates of 0 would be the opposite side of the circle. So imagine a circle being drawn with one side touching (4,0) and the other side touching (-4,0). The diameter would be 4+4 = 8. So what would you imagine is the radius of that circle? Recall radius is half of diameter.

Then sanity check, is this the largest possible circle? Well, any larger means that any other point in the circle will not touch (-4,0) with (4,0) fixed as a point. That means there is no larger circle that will pass through that point (-4,0). The circle with diameter 8 that we had envisioned is the largest.

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Re: Geometry - Máximum Radius   [#permalink] 20 Jan 2014, 11:32
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