A circle has chord PQ. Above the circle (and below it) is a circle tangent to the chord and the large circle. The two inscribed circles are also tangent to each other. The three circle’s centers are collinear. If PQ = 6, what is the area between the two smaller circles and the large circle, shaded in blue?
A circle has two non-intersecting chords AB and CD. Chord RS intersects chord AB at P and CD at Q. If AP = 12, BP = 20, CQ = 10, DQ = 24, and PQ = 14, what is the length of chord RS?
A square has side length equal to 1 meter. A circle is constructed through one corner of the square and tangent to the opposite two sides of the square. What is the area shaded in blue below, which is the area contained by the square and circle excluding the region where the two shapes overlap?
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).
As shown in the diagram below, circle D is internally tangent to circle A and externally tangent to circles B and C.
If circle B has a radius of 2 and C has a radius of 1, what is the radius of circle D?
If the large circle has a radius equal to 12, what is a + b + c?
