2

Part of 2014 Swedish Mathematical Competition

Problems(1)

total area of 3 ext. tangent circles with centers on fourth circle <4\pi R^2

Source: 2014 (-15) Swedish Mathematical Competition p2

Three circles that touch each other externally have all their centers on one fourth circle with radius

R

. Show that the total area of the three circle disks is smaller than

4\pi R^2

geometryareacirclestangent circles