- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Find the area of the square that can be inscribed in a circle of radius $8\ cm$.

**Given:**An square inscribed in a circle of radius $8\ cm$.

**To do:**To find the area of the square.

**Solution:**

Let $ABCD$ be the square inscribed by the circle.

$\therefore$ radius $r=OA=OB=OC=OD=8\ cm$

$ABC$ is a right angled triangle, as $OA=8,\ OC=8$

$AC=8+8=16$

According to Pythagoras theorem,

Square of hypotenuse$=$Sum of squares of other two sides.

$\Rightarrow AC^2=AB^2+BC^2$

As $ABCD$ is a square all the sides are equal, $AB=BC$

$\Rightarrow AC^2=2AB^2$

$\Rightarrow 16^2=2AB^2$

$\therefore AB=8\sqrt{2}$

Therefore, side of the square $=8\sqrt{2}$

Area of square $=( 8\sqrt{2})^2=128\ cm^2$

Advertisements