Property: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.

By the above property,

AE = AD (tangent from A)

AB = AC (tangent from A)

CD = CF (tangent from C)

BF = BE (tangent from B)

Now adding the above equations,

AB + BC + CA = AB + BF + FC + CA

⇒ AB + BC + CA = AB + BE + CD + CA

⇒ AB + BC + CA = AE + AD [∵ AE = AB + BE and AD = AC + CD]

⇒ AB + BC + CA = AD + AD [∵ AD = AE]

⇒ AB + BC + CA = 2AD

Hence, 2AD = AB + BC + CA