- 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, $AB = AC$ and $CP \parallel BA$ and $AP$ is the bisector of exterior $\angle CAD$ of $\triangle ABC$. Prove that $\angle PAC = \angle BCA$.
"
Given:
In the figure, $AB = AC$ and $CP \parallel BA$ and $AP$ is the bisector of exterior $\angle CAD$ of $\triangle ABC$.
To do:
We have to prove that $\angle PAC = \angle BCA$.
Solution:
In $\triangle ABC$,
$AB =AC$
This implies,
$\angle C = \angle B$ (Angles opposite to equal sides)
$\angle CAD = \angle B + \angle C$
$= \angle C + \angle C$
$= 2\angle C$.......….(i)
$AP$ is the bisector of $\angle CAD$
This implies,
$2\angle PAC = \angle CAD$.........…(ii)
From (i) and (ii), we get,
$\angle C = 2\angle PAC$
$\angle C = \angle CAD$
$\angle BCA = \angle PAC$
Hence, $\angle PAC = \angle BCA$.
Advertisements