Thread: circl trig problem

two circles of radii 3 cm and 4dm have their centres 5 cm apart. calculate the area of the region common to both circles.

Formula i use is 1/2r^2(theta - sintheta)

my digram below.. not sure if its correct.. also what angles to i have to find ?


thanks

Originally Posted by smmmc

two circles of radii 3 cm and 4dm have their centres 5 cm apart. calculate the area of the region common to both circles.

Formula i use is 1/2r^2(theta - sintheta)

my digram below.. not sure if its correct.. also what angles to i have to find ?


thanks

The common area consists of two lens-shaped areas.
One lens-shaped area is the difference of the area of a sector and an isosceles triangle.

The triangle CPM is a 3-4-5 right triangle. Therefore



Then the area of the left lens-shaped area is:



To calculate the second part of the common region is left for you.