Challenging Math Problems (Or not)

[lllazar]

All righty, so i like math, specifically geometry, and i wanted to make a page where you can post any tough math problems..then the first person who answers that problem right "wins" a point...those who get 3 points will start being recognized on this page. I will edit this post to show "hall of famers".

3 points: Arithmalete
5 points: Rising Star
10 points: Math God

Hope you guys like this, i'll start off...

A set of integers has an average of 7. When you add the number 10 to the set of integers, the average goes up by 0.5. When you add -3 to the new set of integers, the average goes down by 1.5 (it goes down by 1.5 from the 2nd average, not the original average of 7).

How many integers were in the original set, before anything was added?

[carneyf1d]

5 terms

[lllazar]

Nice carney, here's another one:

Hexagon ABCDEF. Point X outside the hexagon such that AX = BX and ABX is an equilateral triangle.

Circle O is inscribed in Triangle ABX.

Circle Q tangent to ED at the midpoint of ED. Circle Q tangent to lines AF and BC.

Im only using the tangent term to show intersection but only at one point.

What is the ratio of the area of Circle O to Circle Q.

[carneyf1d]

darn. i have autocad on my computer at school. could solve it using that in two seconds, but unfortunately im not there.

[lllazar]

I worked on that one forever when i first saw it.

[carneyf1d]

the circle inside the triangle is 1/4th the size of the circle inscribed in the hexagon.

[carneyf1d]

and i never thought i'd ever have to use heron's formula ever again...

[lllazar]

Sorry that's incorrect

And i think you might have not understood the problem, ill try to to draw it for you.

[andrewwski]

The circle inside the triangle is 1/3 the size of the circle in the hexagon.

[lllazar]

Ok from now on if i post a geometry question, ill post a picture with it, ill have the pic up in a few minutes.

Guys how do i paste a pic to a post directly? I hate having to link you guys to photobucket...

http://s658.photobucket.com/albums/uu30 ... oblem1.png

There you go, the smaller circle is O and the bigger is Q, find the ratio of O to Q