This question was uploaded on 04/10/21 on social media accounts.
A square is inscribed in a semicircle while its base is on the base of the semicircle. A square with a side at end of the diameter of the semicircle and a vertex of the square. Find the area of the square.
Solution 1:
Area:
\[A=S^2=(2\sqrt5)^2+(5-\sqrt5)^2\]
\[A=S^2=50-10\sqrt5\]
Solution 2:
Intersecting chord theorem:
\[(5+x)(5-x)=(2x)^2\]
\[\Rightarrow x=\sqrt5\]
Area:
\[A=S^2=(2\sqrt5)^2+(5-\sqrt5)^2\]
\[A=S^2=50-10\sqrt5\]
Puzzle related to Geometry, Square, Circle, Area.
