Two circles each of radii 1 cm, intersect such that circumference of each circle passes through the center of the others .What is the area of intersecting region?

Question

anonymous · Answer

dude U know calculus???If yes then I may proceed..

anonymous · Answer

i think u can do this by geometry/ trigonometry. by finding the areas of the 2 segments formed by drawing a line between the 2 points of intersection.

anonymous · Answer

the line joining the 2 centres of the circles is perpendicular to this line nd the triangle formed by drawing lines from the circle centres to the points of intersection form an angle of 120 degrees.  Area of secor - area of triangle gives the area of the segment. This X 2 is the area of the intersecting section.

anonymous · Answer

area of sector = 1/2 * 1^2 * 2pi/3 
area of triangle = 1/2 * 1 * 1 * sine 2pi/3 
area of segment = sector - triangle = 0.6142

area of intersection = 2 * 0.6142 = 1.228 to 3 dec places