Notes
four circles in a triangle in a circle solution

Four Circles in a Triangle in a Circle

Solution by Lengths in an Equilateral Triangle

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.