if b is the mean proportion between a and c then prove that a, c, a^2+b^2 and b^2+c^2 are in proportion?

• a,b,c are in proportion => b^2 = ac
  
  =>
  a^2 + b^2 = a^2 + ac = a( a + c)
  b^2 + c^2 = ac + c^2 = c(a + c)
  
  => a / c = a(a + c) / c(a + c)
  => a , c , a(a + c) , c(a + c) are in proportion
  => a , c , a^2 + b^2 , b^2 + c^2 are in proportion.
• 10 years agoHelpfull: Yes(16) No(2)
• farji question...
• 10 years agoHelpfull: Yes(13) No(1)
• since b is the mean proportion b/w a and c
  therefore b^2=ac
  a/c=(a^2+b^2)/(b^2+c^2)=(a^2+ac)/(c^2+ac)
  =a/c
• 10 years agoHelpfull: Yes(0) No(1)