Fdtxjr

Would it be believable to defy demographics in a story?

Friend wants my recommendation but I don't want to

pipe commands inside find -exec?

How to find the largest number(s) in a list of elements?

Does convergence of polynomials imply that of its coefficients?

How are passwords stolen from companies if they only store hashes?

How do researchers send unsolicited emails asking for feedback on their works?

What kind of footwear is suitable for walking in micro gravity environment?

What (if any) is the reason to buy in small local stores?

Should I be concerned about student access to a test bank?

Extraneous elements in "Europe countries" list

Error in master's thesis, I do not know what to do

Hot air balloons as primitive bombers

Why does Surtur say that Thor is Asgard's doom?

Exposing a company lying about themselves in a tightly knit industry: Is my career at risk on the long run?

Emojional cryptic crossword

CLI: Get information Ubuntu releases

label a part of commutative diagram

How can a new country break out from a developed country without war?

Do I need to convey a moral for each of my blog post?

Are hand made posters acceptable in Academia?

Why doesn't the fusion process of the sun speed up?

How to remove space in section title at KOMA-Script

Do I need an EFI partition for each 18.04 ubuntu I have on my HD?

When do three disks in the plane intersect?

Help reducing the following expression involving Heron's formula for the area of a triangle.Radius ratio for four packed circlesTriangle Area problemGeometric inequality $fracR_a2a+b+fracR_b2b+c+fracR_c2c+ageqfrac1sqrt3$Inequality involving inradius, exradii, sides, area, semiperimeterIf $r$ is the inradius of $triangle ABC$,then prove that $frac2r=frac1r_a+frac1r_b+frac1r_c$Three tangent circlesDetermine if 3 circles intersect at a common pointWhat is the area of the intersection of two rings?Prove that in every triangle the inequality $a^3r_a + b^3r_b + c^3r_c ge 8S(2R-r)^2 $ takes place

2

$begingroup$

Suppose $ABC$ is a triangle with $|AB|=c$, $|BC|=a$, $|CA|=b$. Suppose further that $A,B,C$ are the centers of three disks with radii $r_A,r_B,r_C$, respectively.

Is there a sensible algebraic condition (inequality?) involving $a,b,c,r_A,r_B,r_C$ equivalent to the statement "these three disks have nonempty intersection"?

geometry

share|cite|improve this question

asked Mar 13 at 7:20

Michal AdamaszekMichal Adamaszek

2,13659

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Seems like you should be able to do something with the law of cosines here...
  $endgroup$
  – Brian Tung
  Mar 13 at 7:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  One thing is clear that $r_A+r_B+r_C < frac a+b+c 2$ from the diagram.
  $endgroup$
  – Dbchatto67
  Mar 13 at 7:25
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Dbchatto67 I think your inequality must be reversed
  $endgroup$
  – vidyarthi
  Mar 13 at 7:51
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I think the concept of radical centre would be much useful here
  $endgroup$
  – vidyarthi
  Mar 14 at 12:33
  

  
  
  
  

add a comment | 

2

$begingroup$

Suppose $ABC$ is a triangle with $|AB|=c$, $|BC|=a$, $|CA|=b$. Suppose further that $A,B,C$ are the centers of three disks with radii $r_A,r_B,r_C$, respectively.

Is there a sensible algebraic condition (inequality?) involving $a,b,c,r_A,r_B,r_C$ equivalent to the statement "these three disks have nonempty intersection"?

geometry

share|cite|improve this question

asked Mar 13 at 7:20

Michal AdamaszekMichal Adamaszek

2,13659

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Seems like you should be able to do something with the law of cosines here...
  $endgroup$
  – Brian Tung
  Mar 13 at 7:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  One thing is clear that $r_A+r_B+r_C < frac a+b+c 2$ from the diagram.
  $endgroup$
  – Dbchatto67
  Mar 13 at 7:25
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Dbchatto67 I think your inequality must be reversed
  $endgroup$
  – vidyarthi
  Mar 13 at 7:51
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I think the concept of radical centre would be much useful here
  $endgroup$
  – vidyarthi
  Mar 14 at 12:33
  

  
  
  
  

add a comment | 

$begingroup$

Suppose $ABC$ is a triangle with $|AB|=c$, $|BC|=a$, $|CA|=b$. Suppose further that $A,B,C$ are the centers of three disks with radii $r_A,r_B,r_C$, respectively.

Is there a sensible algebraic condition (inequality?) involving $a,b,c,r_A,r_B,r_C$ equivalent to the statement "these three disks have nonempty intersection"?

geometry

share|cite|improve this question

asked Mar 13 at 7:20

Michal AdamaszekMichal Adamaszek

2,13659

$endgroup$

share|cite|improve this question

asked Mar 13 at 7:20

Michal AdamaszekMichal Adamaszek

2,13659

share|cite|improve this question

asked Mar 13 at 7:20

Michal AdamaszekMichal Adamaszek

2,13659

asked Mar 13 at 7:20

Michal AdamaszekMichal Adamaszek

2,13659

asked Mar 13 at 7:20

Michal AdamaszekMichal Adamaszek

2,13659