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4,0) and (-4,0) are the co-ordinates on a circle X. What is [#permalink]
 18 Sep 2003, 12:50
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(4,0) and (-4,0) are the co-ordinates on a circle
X. What is the maximum possible radius of the circle?
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praetorian123 wrote: (4,0) and (-4,0) are the co-ordinates on a circle
X. What is the maximum possible radius of the circle?
These are two points on X-axis and y-coordinates are 0. So, infinite number of circles can be drawn with the center on y-axis as (4,0) and (-4,0) are equidistant from the Y-axis. The smallest circle possible will have a radius of 4. However, I couldn't determine the maximum possible radius. I will wait for others to comment on this. Thanks!
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If there are only two points then the maximum possible radius of a circle is ' Infinity "
u need exactly three points to define a circle.
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abhay pathania
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Edeal
you said there are two points on the X axis.. but these lie ON the CIRCLE.
i think i am missing something big time...can you explain this please?
How will you draw infinite circles passing through the same two points?
We know that the two points lie on the circle and we also know that their y - coordinates are 0
-4,0..........................(0,0)...............................4,0
My question :
Can you show me how the radius is greater than 4 and still the circle passes through both these points.
thanks
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praet.. lets look at the problem this way:
How many circles are possible that have the points A (4,0) & B (-4,0) as its chord. ( a chord is line segment whose end points lie on a circle).
Now consider line segment AB - how many circles can have AB as its chord - infinite.
Also diameter of a circle is always greater in length than the chord (draw and see for urself). So all the circles that i will draw will have diameters greater than this chord length and infinite such circles are possible. The minimum dia ( & radius) is possible when chord itself is diameter of the circle. In that case min. radius = 4.
i hope this clarifies.
-vicks
ps: one question: How many unique solutions does the following system of equations have:
x - 2y = 6
2.5x = 5y + 15
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Vicky wrote: praet.. lets look at the problem this way:
How many circles are possible that have the points A (4,0) & B (-4,0) as its chord. ( a chord is line segment whose end points lie on a circle).
Now consider line segment AB - how many circles can have AB as its chord - infinite.
Also diameter of a circle is always greater in length than the chord (draw and see for urself). So all the circles that i will draw will have diameters greater than this chord length and infinite such circles are possible. The minimum dia ( & radius) is possible when chord itself is diameter of the circle. In that case min. radius = 4.
i hope this clarifies.
-vicks
ps: one question: How many unique solutions does the following system of equations have:
x - 2y = 6
2.5x = 5y + 15
I cant understand why this simple fact slipped my mind
Your question : How many unique solutions does the following system of equations have:
x - 2y = 6
2.5x = 5y + 15 ==> x -2y= 6
Both the equations are the same...Infinite.
Is that correct!
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bingo..!!
we just need to recognize the traps that testmakers want us to fall in... 
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