What is the radius of a circle with center at (4, 3) that is tangential to both the x and y axes?

Expert Answers

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Let the radius of the circle which has its center at (4, 3) and that is tangential to both the x and y axes be r.

As the circle is tangential to the x-axis the distance of the center from the x-axis should be equal to r, here it is equal to 4. This gives the radius r = 4. Similarly, as the circle is tangential to the y-axis, the distance of the center from the y-axis should be equal to r. Here, it is equal to 4. We are getting two different values for the radius, which is not possible.

We can conclude that it is not possible for a circle centered at (4, 3) to be tangential to both the x and y axes.

 

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