Find the ratio of in circle and corcumcircle of an equilateral triangle

• let side of eq triangle be a,
  radius of incircle=a/2*sqrt3,
  radius of circumcircle=a/sqrt3,
  ratio of radius=1/2,
  ratio of areas=1/4
  
• 11 years agoHelpfull: Yes(28) No(1)
• let x = side of equilateral triangle, then:
  A_circumcircle = 1/3 * pi * x^2
  A_incircle = 1/12 * pi * x^2
  the ratio:
  A_incircle / A_circumcircle
  = (1/12 * pi * x^2) / (1/3 * pi * x^2)
  = (1/12)/(1/3)
  = 3/12
  = 1/4
• 11 years agoHelpfull: Yes(8) No(2)
• Since it is a equilateral triangle , the centroid , in certre and circumcenter will lie on same point ....... The centroid divides the median in 1:2 ratio . Hence the radius of incircle and circumcircle will be in the same ratio of 1:2 .
• 11 years agoHelpfull: Yes(6) No(1)
• Ratio of what? Their areas?
• 11 years agoHelpfull: Yes(2) No(0)
• using the formula== A = rs ( where r is inradius and s is semiperimeter)
  and A= abc/4R(R is circumradius)
  r/R=A *4A/s*abc(here a=b=c)
  just put the values we get r/R as 1/2
• 11 years agoHelpfull: Yes(2) No(1)
• Ratio of radius=1/2,
  Ratio of areas=1/4
• 11 years agoHelpfull: Yes(2) No(0)
• let us take the side of equilateral triangle be a
  radius of incircle = a/2sqrt(3)
  radius of circumcircle= a/sqrt(3)
  ratio of radius=1/2
  ratio of are=1/4
• 11 years agoHelpfull: Yes(2) No(0)
• dummy question. there is loss of 5 rupees....and the loss percent is not in d given options
• 11 years agoHelpfull: Yes(1) No(6)
• ratio of radii r:R=1:2
  ratio of areas a:A=1:4
• 11 years agoHelpfull: Yes(1) No(0)
• 1:2
  radius of in circle=(a/2(3^(1/2)))
  and radius of curcumcircle=(a/(3^(1/2))
• 11 years agoHelpfull: Yes(0) No(0)