Circle A has a center at #(1 ,3 )# and an area of #16 pi#. Circle B has a center at #(2 ,7 )# and an area of #28 pi#. Do the circles overlap?
1 Answer
The distance from the centre of circle A to the centre of circle B is less than the sum of the two radii. Thus we can conclude that the two circles are overlapping.
Explanation:
area of a circle =
area of circle A
area of circle B
radius of circle A =
radius of circle B
If the circles are just touching, the distance between their centres will be:
The distance from the centre of circle A to the centre of circle B = d
Using Pythagorus's theorem:
d is less than the sum of the two radii. Thus we can conclude that the two circles are overlapping.
They actually overlap a lot as the centre of circle A is within circle B (because