# Four Circles in a Triangle in a Circle +-- {.image} [[FourCirclesinaTriangleinaCircle.png:pic]] > Four identical circles are packed into an equilateral triangle. What fraction of the larger circle is shaded? =-- ## Solution by [[Lengths in an Equilateral Triangle]] +-- {.image} [[FourCirclesinaTriangleinaCircleLabelled.png:pic]] =-- In the above diagram, $O A$ is a radius of the outer circle. Triangle $A C B$ is half an [[equilateral triangle]] so the length of $C A$ is twice that of $C B$, which is a radius of one of the small circles. Therefore, the length of $O A$ is four times that of $C B$. Since the [[area scale factor]] is the square of the length [[scale factor]], the area of the outer circle is $16$ times that of one of the small circles. Therefore, one quarter of the larger circle is shaded.