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    Explanation of how to find the tangent line to a circle

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    ** Please see the attached PDF document for the full problem description **

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    ** Please see the attached file for the complete problem description **

    (a) The first sentence is just background. There is a circle and there is a line. Equations for both are given.

    i) they want you to show that (please see the attached file) and (please see the attached file) are tangent to the circle.

    Really that means find d such that the line with slope -1 and equation x + y = d is tangent to the circle.

    What does it mean for the lines to be tangent to the circle?
    1) they touch the circle at only one point
    2) the derivative for the circle at that point has the same value as the slope of the line.

    So now, find d on your own using the fact that the above conditions must hold.

    Satisfy Condition 2) By finding the ...

    Solution Summary

    This solution includes the steps to finding the tangent line to a circle, the steps to finding intersection points, and the steps to finding a value that will maximize the area of a triangle. Additionally, it includes an explanation of what it means to be: an odd function and a decreasing function, an explanation as to how to take a limit at infinity, and an explanation of when a function has an inverse and how to find the domain of the inverse function.