Two large circles are tangent to each other and the parallel lines. Two small circles are tangent to the large circles and to one of the lines. If the distance between the centers of the small circles is 96, what is the distance between the centers of the large circles?
A square contains a semicircle and a quarter circle, as shown. The two circles are tangent to each other. The semicircle has a diameter equal to 12 and the quarter circle has a radius equal to 12. What is the area of the square? What is the length of the tangent line segment AB?
I have 3 unit circles. Two of them are externally tangent to each other. The third one passes through the tangent point, cutting two symmetrical areas from those two circles, as shown in the diagram. What is the shaded area?
Three congruent circles are pairwise tangent and each has a radius equal to 2. A circle circumscribes the three circles. Calculate the total area shaded in blue. The blue region is comprised of two parts. One region is the three circular sectors of the small circles enclosed by the line segments connecting the three small circle’s centers. The other region is outside the three small circles and bound by the large circumscribing circle (exclude the area in between the three small circles).
Three spheres are tangent to a plane at the vertices of a triangle and are tangent to each other. Find the radii of the spheres if the sides of the triangle are 6, 8, and 10.
