- 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
Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.
To do:
We have to prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.
Solution:
Let two circles with centres $A$ and $A'$ intersect each other at $B$ and $B'$ respectively.
In $\triangle BAA’$ and $\triangle B'AA’$
$AB = AB'$ (Radii of circle with centre $A$)
$A’B = A’B'$ (Radii of circle with centre $A'$)
$AA’ = AA’$ (Common side)
Therefore, by $SSS$ congruency,
$\triangle BAA’ \cong \triangle B'AA’$
This implies,
$\angle ABA' = \angle AB'A’$
From above,
The line of centres of two intersecting circles subtends equal angles at the two points of intersection.
Hence proved.
Advertisements