CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

In the given circle, O is the centre of the circle and AD, AE are the two tangents. If BC is also a tangent, then which of the given options is true?

 



Your Answer
A

AC + AB = BC 

Your Answer
B

3AE = AB + BC + AC

Your Answer
C

AB + BC + AC = 4AE 

Correct Answer
D

2AE = AB + BC + AC 


Solution

The correct option is C

2AE = AB + BC + AC 


From the figure,
AE = AB + BE

BE = BP (Tangents from an external point to a circle are equal in length)

Therefore, AE = AB + BP   …(i)

Also, AE = AD (Tangents from an external point to a circle are equal in length)

AE = AC + CD

But CD = CP (Tangents from an external point to a circle are equal in length)

Therefore, AE = AC + CP  ….(ii)

On adding the equations (i) and (ii), we get,

2AE = AB + BP + AC + CP

Since, BP+CP = BC, 
2AE = AB + BC + AC   

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image