Geometry: Given 2 pts on, line tangent to circle, find center, radius

[Sameir7]

 

[Dr.Peterson]

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I can't read the picture. Please try uploading it again, making sure it is sized appropriately; and type the words of the problem so we can be sure what it says.

 

[stapel]

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As near as I can tell, the exercise gives you the coordinates of two points (A and B) on the circle, along with a line which is tangent to the circle. You are asked to find the center and radius of the circle.

I think they gave you coordinates for the points and an equation for the line, but this information is too small to be legible. Please reply with that info, along with a clear listing of your thoughts and efforts so far, so we can see what's going on. Thank you!

 

[mmm4444bot]

I can see from the image that all quantities are symbolic. That's not enough information to guarantee a unique solution. Are you sure there's no other known information?

The given tangent line is:

a·x + b·y + c = 0

The coordinates for the given points appear to be subscripted symbols for x and y, but I cannot read the subscripts. I'll use letters:

A(x_A, y_A)

B(x_B, y_B)

Here's an example of given coordinates for points A and B, along with given parameters (estimated) for the tangent line:

x_A = 1/3 + 2·√2/3

y_A = 4·√2/3 - 5/3

x_B = 11/17 + 18·√2/17

y_B = 4·√2/17 - 7/17

a ≈ 1.39814951

b = -1

c ≈ -7.24185978

With these givens, either of the following is possible.

A circle of radius 4 centered at (3, 1+2√2)

A circle of radius √5 centered at (1, -2)

In this example, how would we determine which circle they're talking about?