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Question

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


A
3AE = AB + BC + AC
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B
AB + BC + AC = 4AE
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C
2AE = AB + BC + AC
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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)

And, AD = 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


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