The Star Medallion
Geometry
Level
4
A star is inscribed inside a circle with radius \(r\) as shown in the picture above. The formula that puts the area of the star \(S\) in terms of the circle's radius \(r\) can be expressed as follows:
\[ \large S = \dfrac{a \sqrt{10a-b\sqrt a}}c r^2 \; , \]
where \(a,b\) and \(c\) are positive integers with \(a\) square-free and \(a,c\) coprime.
Find the value of \(a+b+c\).
by
Ruben Calzadilla-Badra