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?

• A. AC + AB = BC
• B. 3AE = AB + BC + AC
• C. AB + BC + AC = 4AE
• D. 2AE = AB + BC + AC

Answer 1

The correct option is D

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