# Math Help - circl trig problem

1. ## 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

2. 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

$\sin\left(\dfrac{\mu}2\right)=\dfrac35~\implies~\m u \approx 73.74^\circ$

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

$A=\underbrace{\dfrac{\mu}{360^\circ} \cdot \pi \cdot 4^2}_{sector} - \underbrace{\dfrac12 \cdot 4^2 \cdot \sin(\mu)}_{isosceles\ triangle} \approx 2.616$

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