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?
In a unit square, two quarter circles are drawn, centered at two opposite vertices, What is the area of the oval-shaped region?
In a square with a side length of 1, two quarter circles are drawn and a circle is inscribed between the quarter circles, as shown in the diagram. What is the radius of the inscribed circle?
A circle contains 4 identical squares, as shown below. If each square has a side length equal to 2, what is the radius of the circle?
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).
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?
