This question was uploaded on 02/10/21 on social media accounts.
A semicircle is placed on a side of a square and a line from one vertex of the square to the midpoint of a side such that it passes through the circle. Find the length of the line drawn from the end of the semicircle to the side of the square such the line passes through the cutting point.
Solution 1:
\[tan(2\theta)=\frac{10}{5}=2\]
\[tan(\theta)=\frac{\sqrt{5}-1}{2}\]
Also,
\[tan(\theta)=\frac{a}{10}\]
\[\Rightarrow a=5(\sqrt{5}-1)\]
Now,
\[x^2=a^2+10^2\]
\[\Rightarrow x=5\sqrt{10-2\sqrt{5}}\]
Solution 2:
Length of the blue line (L) :
\[L^2=(5\sqrt5-5)^2+10^2\]
\[\Rightarrow L=5\sqrt{10-2\sqrt{5}}\]
Idea of this solution is from "@lucker0_0" on Instagram.
Question based on Geometry, Square, Circle.
