- #1

Saracen Rue

- 150

- 10

**Summary::**Calculate the percentage of area remaining when a quarter-cirlce is deprived of 1 large circles and 2 smaller circles.

Hi,

I'm not sure if this is the right subforum for this question but it seemed to be the one that fit the best. Please consider the following diagram:

Before continuing, let's quickly define a few things:

$$r_{q} = \text{ radius of the quarter-circle}$$

$$r_{b} = \text{ radius of the big circle}$$

$$r_{s} = \text{ radii of the two smaller circles}$$

I figured out how to express ##r_{q}## in terms of ##r_{b}## with relative ease. With the help of a little Pythagoras I managed to come to the conclusion that

$$r_{q} = (\sqrt{2} + 1) \cdot r_{b}$$

This is a good start, however here's where I hit a brick wall. I have no idea how to go about expressing ##r_{s}## in terms of ##r_{b}##. I've tried everything I can think of but I just can't seem to make any progress at all. Any help with solving this problem is greatly appreciated.

Thank you all for your time.

**[Moderator's note: Moved from a technical forum and thus no template.]**

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