This question was uploaded on 07/10/21 on social media accounts.
A semicircle is placed in a quarter-circle. The diameter of the quarter circle is the same as the radius of the quarter-circle.
Solution 1:
\[r^2+1^2=(2r)^2\]
\[\Rightarrow r^2=\frac{1}{3}\]
\[\Rightarrow Area=\frac{\pi}{2} r^2=\frac{\pi}{6}\]
Solution 2:
Intersecting chord theorem assuming complete circle:
\[(r)(3r)=1^2\]
\[\Rightarrow r^2=\frac{1}{3}\]
\[\Rightarrow Area=\frac{\pi}{2} r^2=\frac{\pi}{6}\]
Puzzle related to Geometry, Circle, Area.
