Two circles of radii 3cm and 4cm have their centres 5cm apart. Calculate the area common to both circles correct to 2 decimal places.
we use minor segments but I'm not getting the answer 6.64cm squared
The triangle joining one point of intersection and the 2 centres is a right-angled triangle because the sides are 3, 4 and 5 , a Pythagorean triple. With the other point of intersection, you form an identical triangle. The 2 points of intersection form a sector with each centre. So you can work out the areas of the 2 sectors, using A = 0.5 x r^2 x theta. The 2 said triangles have, apart from thr right angle, 2 angles A and B say. You can easily find A and B using basic trigonometry. The theta for each sector = 2A and 2B resp. The line segment joining the 2 points of intersection form a triangle with each centre. The required area = area of sector - area of its associated triangle PLUS area of other sector - area of its assoc triangle.
By the way: this is not quite a circle geometry question.
