For those bored, a little math puzzle

1. Jan 14, 2009

LennoxLewis

What is the radius of the largest circle that you can fit in one quadrant of a bigger of radius 1?

2. Jan 14, 2009

SticksandStones

Real quick, I'm going to say sqrt(2)/4.

3. Jan 14, 2009

Gokul43201

Staff Emeritus
1/(1+sqrt(2))

PS: aka sqrt(2)-1

Last edited: Jan 14, 2009
4. Jan 14, 2009

Topher925

Rsmall = Rlarge x (20.5-1)

5. Jan 15, 2009

LennoxLewis

Good work, how did you get to it?

6. Jan 15, 2009

Gokul43201

Staff Emeritus
Let the radial position of the center of the incircle be x. From symmetry, this center must lie on the radial line that bisects the angle of the quadrant, i.e., the line at angle pi/4. Draw two radii of the small circle: one ending on the arc of the quadrant (running along this line at pi/4) and the other ending on one of its two arms (running normal to the arm). Equating these radii gives you 1-x=x/sqrt(2), and the radius of the incircle, r=1-x.

7. Jan 15, 2009

LennoxLewis

Right, i used a similar but less effective way. By similar means, i set up the equation (1 - x)^2 = x^2 + x^2, asin Pythagoras's rule for that triangle.