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 fig., PA and PB are two tangents drawn from an external point P to a circle and radius 4 cm. if PA$\perp $PB, then the length of each tangent is:
$( A) \ 3\ cm$
$( B) \ 4\ cm$
$( C) \ 5\ cm$
$( D) \ 6\ cm$"
Given: A circle with radius 4 cm, and two tangents PA and PB drawn to the circle from an external point P. And $PA\bot PB$
To do: To find the length of the tangents PA and PB.
Solution:
As given,
PA and PB are tangents to the circle at the points A and B respectively, from the exterrnal point P.
$\therefore PA=PB$, $( tangents\ drawn\ to\ a\ circle\ from\ an\ external\ point\ have\ equal\ length.)$
$\therefore CA\perp PA\ and\ CB\perp PB$
$\because$ Radius is always perpendicular to the tangent at the point of contact.
and $PA\bot PB$ $( given\ in\ the\ question)$
$CA=CB=$Radius of the circle
$\therefore$ APBC is a square having equal side 4 cm.
The length of eachh tangent is 4cm.
Therefore option $( B)$ is correct.
Updated on: 10-Oct-2022
103 Views
Advertisements