Q. 134.2( 6 Votes )

In Fig. 10.78, if

Answer :

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

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