The diameter of a Circle is 18 cm , triangle is inscribed inside the circle . another circle in inscribed in that triangle whose radius in 6 cm. find the perameter of the triangle.

• if diameter of the circle being largest side of the right angled triangle
  then let two sides of triangle be x,y
  
  1/2 *xy = (x+y+18)/2 * 6
  => xy = 6(x+y) + 108
  
  x^2 + y^2 = 18^2
  => (x+y)^2 - 2xy - 324 = 0
  => (x+y)^2 - 12(x+y) - 216 - 324 = 0
  => (x+y)^2 - 12(x+y) - 540 = 0
  => (x+y-30)(x+y+18)= 0
  => (x+y)= 30
  perimeter = x+y+18 = 30 + 18 = 48
• 9 years agoHelpfull: Yes(11) No(2)
• if diameter of the circle being largest side of the right angled triangle.
  in triangle ABC,B is right angle
  R=9cm
  r=6cm
  circumradius (R) = Hypotenuse/2
  R=AC/2
  9=AC/2
  AC=18cm
  r=(AB+BC-AC)/2
  6=(AB+BC-18)/2
  AB+BC=30
  s=(AB+BC+AC)/2
  perimeter = 2s
  ......perimeter of the triangle = 42.
• 9 years agoHelpfull: Yes(1) No(0)
• i think the smaller circle should have diameter as 6 not radius ,
  If such is the case then answer is 54
• 9 years agoHelpfull: Yes(1) No(3)
• Question slight modification there..diameter of the circle being largest side of the right angled triangle...
• 9 years agoHelpfull: Yes(0) No(0)