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?
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