- 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
In the figure, common tangents $ P Q $ and $ R S $ to two circles intersect at $ A $. Prove that $ P Q=R S $."
Given:
In the figure, common tangents \( P Q \) and \( R S \) to two circles intersect at \( A \).
To do:
We have to prove that \( P Q=R S \).
Solution:
$AQ$ and $AR$ are two tangents drawn from $A$ to the circle with centre $O$.
$AP = AR$....….(i)
Similarly,
$AQ$ and $AS$ are the tangents to the circle with centre $C$.
$AQ = AS$....….(ii)
Adding (i) and (ii), we get,
$AP + AQ = AR + AS$
$PQ = RS$
Hence proved.
Advertisements