# Using differentiation to find maximum length problems

## Homework Statement

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.

## 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.

#### Attachments

• image.jpg
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Dick
Homework Helper

## Homework Statement

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.

## 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.

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

check out the attachment, does that seem right?

#### Attachments

• image (1).jpg
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Dick
Homework Helper
check out the attachment, does that seem right?

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.

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

HallsofIvy
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 $\sqrt{1- x^2}$.