Using differentiation to find maximum length problems

1. Feb 14, 2013

lmstaples

1. The problem statement, all variables and given/known data

The line segment AB lies on a diameter of a circle of radius 1, and the angle BAC is a right angle.

Find the greatest possible value of the sum of the lengths of AB and AC.

2. Relevant equations

3. The attempt at a solution

I have no idea what parameters to use or how to set up the problem.

Any help would be much appreciated.

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2. Feb 14, 2013

Dick

Why not try picking the parameter to be the x coordinate of A?

3. Feb 14, 2013

lmstaples

check out the attachment, does that seem right?

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4. Feb 14, 2013

Dick

Well, you ignored my advice on which parameter to use, so apparently you weren't all that confused to begin with. Yes, it looks ok.

5. Feb 14, 2013

lmstaples

Haha sorry, I had so many ideas of ways to do it and that's the only one I managed to fully work through :)

6. Feb 15, 2013

HallsofIvy

Staff Emeritus
Here (I think) is what Dick was suggesting: set up a coordinate system so the origin is at the center of the circle, A is at (-1, 0), and the y-axis is parallel to BC. Then AB has length x+ 1 and BC has length $\sqrt{1- x^2}$.

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