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?
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?
Triangle ABC is inscribed in a circle. Construct chord AD and let E be the intersection of chords AD and BC. If AB = AC = 12 and AE = 8, then what is the length of AD?
A circle of radius 1 is tangent to the parabola y=x^2 as shown. Find the gray area between the circle and the parabola?
