2 circles intersect each other at 2 points P and Q .smaller circle has radius 1 cm.if arc extended by smaller circle is 90 degree and that of the larger circle in 60 degree at their corresponding centres.Find out the common area of the circles??

• from diagram,
  radius of smaller circle = 1 cm
  radius of larger circle = √2 cm
  
  common area = area of sector 1 + area of sector 2 - area of quadilateral
  = pi*(√2)^2*60/360 + pi*1^2*90/360 - [√3/4 *(√2)^2 + 1/2 *1*1]
  = pi/3 + pi/4 - (√3+1)/2
  = pi*7/12 - (√3+1)/2
  = 0.464 cm^2
  
• 10 years agoHelpfull: Yes(15) No(1)
• correction 7π/12 - (√3+1)/2 or 0.466 sq cms
  
  smaller circle's center and PQ is making a right angled triangle with 45,45 angles and the larger circle's center and PQ is making a equilateral triangle with side √2 (deduced by drawing the figure).
  Then, adding the two triangles areas and subtracting alternately the two sectors of 90degre and 60degree, we can calculate the common area in between
  
• 10 years agoHelpfull: Yes(1) No(0)
• hai rakesh, how [√3/4 *(√2)^2 + 1/2 *1*1] is became?
• 10 years agoHelpfull: Yes(1) No(0)
• radius of larger circle ,R=2^1/2
  radius of small circle r=1
  then,
  common area=(pi x 1 x 1)/4-1/2*1*1+ pi*2/6-(1/2*2*1/2*(3)^1/2)
  =pi*7/12-(1+3^1/2)/2
• 10 years agoHelpfull: Yes(0) No(2)
• smaller circle's center and PQ is making a right angled triangle with 45,45 angles and the larger circle's center and PQ is making a equilateral triangle with side √2 (deduced by drawing the figure).
  Then, adding the two triangles areas and subtracting alternately the two sectors of 90degre and 60degree, we can calculate the common area in between
  ANS: π/3 - (√3-1)/2 or 0.681 sq cms
• 10 years agoHelpfull: Yes(0) No(3)
• Hello I have small doubt regarding radius of second circle
  length of arc = (90(deg) * 2 * pi * 1 /360 ) = ( 60 * 2 * pi * r/360) if above is correct then we get radius of second is 1.5
  
• 10 years agoHelpfull: Yes(0) No(2)
• 7*3.14/12 - (1.732+1)/2
  
• 9 years agoHelpfull: Yes(0) No(0)