Question

Whoever solves this easy question first gets a medal:

https://docs.google.com/file/d/0B4A27kix-0naTkxiVmhCOXJmWDg/edit?usp=sharing

You have 15 minutes. Your time begins now.

Answer 1

Do I see people giving up already?

Answer 2

1 minute to go.

Answer 3

You don't need to type up a solution; just the answer.

Answer 4

Your time is now over. Please put your pencils down.

Answer 5

Or finish up whatever you're typing quickly.

Answer 6

BE is the geometric mean of AB and BC

\(\sqrt{3} = \sqrt{AB.BC}\)

\(3 = AB.BC\) -----------------(1)

area of shaded region = area of outer circle - are of inner circles
= pi.(AB+BC/2)^2 - [pi(AB/2)^2 + pi(BC/2)^2]
= pi/4[(AB+BC)^2 - AB^2 -BC^2]
= pi/4[2AB.BC]
= pi/4[2.3]
= 3pi/2

Answer 7

That is correct. Good job.

Answer 8

u giveing a test..

Answer 9

oh ty !

Answer 10

No, just testing. It's a pretty simple question, I found 3 different ways of solving it, or may be 2. I just wanted to see how the people here do at solving it within 15min ;P

Answer 11

ohk.. good q :)

Answer 12

Competition now over. @ganeshie8 wins.

Answer 13

Oh wow my bizarro method of using similar triangles actually worked :O

Answer 14

wow thats great.. guess similar triangles, pythagora + solving equations also lead to 3=AB.BC kinndof relation which we can sub in the end..

Answer 15

I'm gonna neaten it up and post it for anyone who's curious on the similar triangles method. My original work was all over the place.

Answer 16

K @agent0smith

Answer 17

@ganeshie8 yes, I used pythag + similar triangles.

Since I didn't put it on my working, diameter of the outer circle is a+x, smaller ones are a and x.

Answer 18

I didn't think I could solve for the area, without x... until all the x's magically disappeared!

Answer 19

Also @ganeshie8 yes, the 3=ax that I derived is really 3=AB.BC.

Answer 20

Good job to you as well :D

Answer 21

You went through too much work to figure AB X BC = 3. You could've just used the intersecting chords theorem to figure that out in 1 second. But it's ok ;) It's always nice to figure things out manually by yourself.

Answer 22

I don't remember too many geometry theorems :P