This question was uploaded on 05/10/21 on social media accounts.
A semicircle is inscribed in a square such that its base is on one of the square's sides. Two lines from both edges of the diameter of the semicircle are drawn to midpoints of two of the sides of the square.
Solution:
\[\tan(\theta)=\frac{1}{2}=\frac{c}{a}=\frac{d}{c}\]
Also,
\[a+d=c+b\]
From above two cases,
\[\Rightarrow a=4d,⠀b=3d,⠀c=2d\]
\[\Rightarrow a:b:c:d=4:3:2:1\]
Puzzle related to Geometry, Square, Ratio.
