# Intersection of circles

• May 21st 2009, 01:08 AM
CipherPol
Intersection of circles
Started learning arcs, secotr and segments of circles, but textbook doesn't explain this problem.

Two circles of radii 3 cm and 4cm have their centres 5 cm apart. Find the area of the intersection of the two circles.

Thanks.
• May 21st 2009, 07:20 AM
Opalg
Quote:

Originally Posted by CipherPol
Started learning arcs, secotr and segments of circles, but textbook doesn't explain this problem.

Two circles of radii 3 cm and 4cm have their centres 5 cm apart. Find the area of the intersection of the two circles.

http://www.thelances.co.uk/imagesC/lens.jpg
In the picture, you want the area of the region CXDY. Split it into two by the line CD. The part to the right of that line is equal to the sector ACXD of the smaller circle, less the triangle ACD. Similarly, the part to the left of the line is equal to the sector BCYD of the larger circle, less the triangle BCD.

You will doubtless have noticed that ACB and ADB are 3-4-5 right-angled triangles, which will be helpful in calculating the angles that you require in order to find the areas of those sectors and triangles.