Question

In the given circle, O is the center of the circle and AD, AE are the two tangents. BC is also a tangent, then:

(a) AC + AB = BC 

(b) 3AE = AB + BC + AC 

(c) AB + BC + AC = 4AE 

(d) 2AE = AB + BC + AC

Answer 1

Answer : (d) 2AE = AB + BC + AC 

Since the lengths of the tangents from the same external point are equal, CD = CP and BP = BE. 

Also, AE = AD 

Now AD = AC + CD = AC + CP ...(i) 

AE = AB + BE = AB + BP ...(ii) 

∴ Adding eqns. (i) and (ii), we get 

AD + AE = AC + CP + AB + BP ( ∵ AD = AE) 

⇒  2AE = AB + BC + AC.