Get Answers to all your Questions

header-bg qa

Prove that the lengths of the tangents drawn from an external point to a circle are equal 

 

 

 

 

 
 
 
 
 

Answers (1)

Tangent AB and AC OB and AC are radius 

To prove AB = AC 

proof 

As AB is tangent 

= AB \perp OB \\\\ \angle OBA = 90 \degree

= AB \perp OB \\\\ \angle OBA = 90 \degree

Hence \Delta OBA is a right-angled triangle 

similarly 

Hence \Delta OCA is also a right-angled triangle 

In \Delta OBA and \Delta OCA

\angle OBA = \angle OCA \\\\ OA = OA \\\\ OB = OC

BY RHS congruency \angle OBA \cong \angle OCA \\\\

Hence by CPCT 

AB  = AC 

Hence proved 

 

Posted by

Ravindra Pindel

View full answer