1. ## Modern Art

Jezza Bear went to the Tat Modern in the Magic Forest with Wize Old Olly the Owl this weekend and they went through various galleries until they came to a picture that got Olly thinking.

"JB you see that picture there, the one with the circle and the rectangle. Now from my observation that is a perfect circle and a perfect square, now if that were true and the grey rectangle is 8 units by 16 units, what is the area of the red bit of the picture?"

As they were in the Tat Modern, he was not allowed to touch the painting or measure it.

JB got the answer after a nice <img src=/S/coffeetime.gif border=0 alt=coffeetime width=32 height=48>. Can you work out the answer?

2. ## Re: Modern Art

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Denote the radius of the circle by r. From the gray rectangle, we can deduct (r-8)^2 + (r-16)^2 = r^2. The solutions of this equation are r=8 and r=40. The radius must obviously be larger than 16 (the long side of the rectangle), so the relevant solution is r=40.
The area of the square is 80^2 = 6400, that of the circle is pi*40^2 = 1600*pi. The area of the red bit is one quarter of the difference, or 1600-400*pi ~ 343.36 (square units)</span hide>

<img src=/S/whisper.gif border=0 alt=whisper width=29 height=17> Does the red bit represent what's left of Labour in the Magic Forest after the recent elections? <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

3. ## Re: Modern Art

Very good fine sir, you get [free tickets] to the Tat Modern...
<img src=/S/whisper.gif border=0 alt=whisper width=29 height=17>......definitely true....Olly got the larger amount of votes represented by the circle <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

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