Tuesday, Math 7th

[Lara Hulbert]

Find the ratio of the circle's radius to the triangle's side length. 

[joshuaw.bartlett]

R = (sqrt(3)-1)/A

 

where R is the rasius of the circles, and

A is the length of one side of the triangle

 

 

[joshuaw.bartlett]

Whoops.  Typo. 

 

R = (sqrt(3)-1)A/4

[msshehane]

I found the same answer as sir Josh.

[Gregory M. Hulbert]

[Lara Hulbert]

Dad, did you post something? I can't see your response. 

In yours Michael, what length is x? 

I approached it a different way but got the same answer as you guys! Then I also decided I write up a formal proof. There are probably some steps in logic missing though. 

[Lara Hulbert]

Actually never mind, Dad. I figured it out. To you and to Josh, do you need to prove that the the segment that extends out from the edge of the circle to the nearest vertex of the triangle is equal to the radius? I'm not sure. 

[Lara Hulbert]

And I've had everyone at school working on this today too.. 

Coworker Andrew: 

Coworker Seth: 

[Gregory M. Hulbert]

Did you see my image in the post after Michael's? Which triangle are you referring to about "the segment that extends out ...."?

[joshuaw.bartlett]

My determination that the top segment (I've named it 'h') comes from the bottom right diagram. The 30-60-90 triangle formed there consists of a hypotenuse of R+h and a short leg of R. Since that ratio is 2:1, R+h=R*2. Thus h=R.

[Michael]

The length I defined as x was the side of the right triangle I created by making a triangle whose hypotenuse was the distance between the center of two circles.  I drew the triangle, but it might be hard to see on my picture.  This triangle was the same as the one I drew up in the top of my picture to find y.  They were both 30 60 90 triangles with one side r and the hypotenuse 2r.

Sent from my iPhone

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