(a) Three circles (of radius 1, 2 and 3) are placed so that each is tangent to the other two. What is the area of the triangle whose vertices are at the centres of the circles?

(b) Three circles of radius 1 are placed so that each is tangent to the other two. What is the area of the largest circle that fits in the space between them?

(c) Two circles, of radius 3 and 4, are placed so that they overlap with a distance of 5 between their centres. What is the distance between their points of intersection?