Radius of the circle

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Pramod Kumar Tandon

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Find Radius of the circle passing through (10,2) and touching the circle (x-1)^2 + y^2 = 18 externally. I am just unable to solve it.
 
Pramod Kumar Tandon said:
Find Radius of the circle passing through (10,2) and touching the circle (x-1)^2 + y^2 = 18 externally. I am just unable to solve it.
Click to expand...
First an approximate sketch of both the circles would be useful. We would note that the centers of the circles and the point of tangency will be on the same straight-line.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
Can I not do a simple calculus problem or are these numbers messy?
 
I used Geogebra to draw the figure. I found many ( may be infinite number) of circles passing through (10,2) and touching the given circle. So I think I must add at least one more point ( say 9,-1 ) to the question to get a single answer. But then how should I proceed ?
The revised question will be : Find Radius of the circle passing through (10,2) and (9,-1) and touching the circle (x-1)^2 + y^2 = 18 externally. I am just unable to solve it.
 
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I have used Geogebra to draw this figure. From there I have realized that infinite no of circles can be drawn using the given Data. In order to get a single answer, we must choose at leat one more point on the required circle. Let's choose the second point as (9,-1)
 
Pramod Kumar Tandon said:
I used Geogebra to draw the figure. I found many ( may be infinite number) of circles passing through (10,2) and touching the given circle. So I think I must add at least one more point ( say 9,-1 ) to the question to get a single answer. But then how should I proceed ?
The revised question will be : Find Radius of the circle passing through (10,2) and (9,-1) and touching the circle (x-1)^2 + y^2 = 18 externally. I am just unable to solve it.
Click to expand...
You're right. I assume you copied the problem exactly as given?

I can choose any point B on the circle as the point of tangency, and construct a circle satisfying the requirements (though more than half of such points will result in internal tangency):

1659529862044.png​

There is a minimum radius for this circle; could that be what they intended?
 
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