![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
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
If the angle between two tangents drawn from an external paint P to a circle of radius a and center O, is $60^{o}$, then find the length of OP.
Given: Radius of the circle $=a$ and angle between the two tangents drawn from external point $P=60^{o}$
To do: To find the length of OP.
Solution:
![](/assets/questions/media/148618-33683-1607069614.png)
Given that $\angle BPA=60^{o}$
$OB=OA=a \ \ \ \ \ \ \ \ ( \ radii\ of\ the\ circle)$
$PA=PB\ \ \ \ \ \ [ length\ of\ tangents\ Equal\ OP=OP]$
$\vartriangle PBO$ and $\vartriangle PAO$ are congruent. [ By SSS congruency]
$\angle BPO=\angle OPA\ =\frac{60^{o}}{2} =30^{o}$
In $\vartriangle PBO$ ,
$sin\ 30^{o} =\frac{a}{OP}$
$\Rightarrow \frac{1}{2} =\frac{a}{OP}$
$\Rightarrow OP=2a\ units$
Advertisements