Finding Common Area of Two Circles

[z.js]

Homework Statement

Two circles with radii 12 cm and 10 cm respectively have their centers 14 cm apart, find the area common to both circles. (note : This is in radians.)

Homework Equations

Area of a sector = 0.5r²θ - 0.5r²sin θ

The Attempt at a Solution

None.

 

[LeonhardEu]

Just decompose the problem. The formula you have in 2 is the area of a SEGMENT when the central angle is θ. Split the common area as the sum of segments of cycles. So the only thing remaining is to find the central angles. This is to be done using the radius and the distance between the two cycles using the cosine law. These for you to get started. I'll make now a figure to show you exactly what i mean. Sorry but this is my first post ;)

 

[NascentOxygen]

Two circles with radii 12 cm and 10 cm respectively have their centers 14 cm apart, find the area common to both circles. (note : This is in radians.)

Hi z.js,

ditto to LeonhardEu

I'm sure you are not trying to do this without drawing a large diagram. But it's difficult to give hints when you haven't provided your sketch. On the intersecting circles diagram, you can draw in a triangle of sides 12, 10 and 14 cm. First step, determine two of its angles (yes, in radians).