Question:
If AD,AE and BC are tangents to the circle at the point of contact D,E and F then a)AD=AB C CA,b)2AD=AB BC CA,c)3AD=AB BC CA,d)4AD=AB BC CA
Answer:
We know that tangents drawn from a point out side the circle are equal in length.
From the figure,
AD = AC + CD
=> AD = AC + CF ..........1 {since CD = CF }
AE = AB + BE
=> AE = AB + BF ..........2 {since BE = BF}
From equation 1 and 2, we get
AD + AE = AC + CF + AB + BF
=> AD + AE = (AB + AC) + (BF + CF)
=> AD + AE = AB + AC + BC {since BC = BF + CF}
=> AD + AD = AB + AC + BC {since AE = AD}
=> 2AD = AB + BC + CA
So, option 2 is correct
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