This question was uploaded on 21/11/21 on social media accounts.
Solution:
The radius of the quarter circle is 5 by the hypotenuse theorem.
Let the radius of the small circle be 'r'.
\[(5-r)^2=r^2+(3+r)^2\]
\[\Rightarrow r = 4\sqrt5-8\]
Area:
\[A= \pi r^2 = (144-16\sqrt5)\pi\]
or
\[A= 16(9-4\sqrt5)\pi\]
