Notes
circles in triangle and rhombus solution

Circles in Triangle and Rhombus

Solution by Lengths in an Equilateral Triangle and Area Scale Factor

The diameter of the circle inside the rhombus, $E D$, has the same length as the height of the equilateral triangle, $C B$. From the relationships between the lengths in an equilateral triangle, the length of $O B$ is one third that of $C B$. The radius of the circle in the rhombus is therefore $\frac{3}{2}$ times that of the circle in the triangle. The area scale factor is then $\frac{9}{4}$ and so its area is $\frac{9}{4} \times 16 = 36$.