A tower ABCD stands on a level ground with foot A . At a point P on the ground, the portion AB,AC and AD subtends angles α,β and γ respectively. If AB=a,AC=b,AD=c,AP=x and α+β+γ=180° , then (a+b+c)x2=
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a
abc
b
1abc
c
a + b - c
d
a - b - c
answer is A.
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Detailed Solution
From, ΔPAB,tanα=ax From, ΔPAC,tanβ=bx From, ΔPAD,tanγ=cx Given α+β+γ=180⇒tanα+tanβ+tanγ=tanαtanβtanγ⇒ax+bx+cx=abcx3⇒(a+b+c)x2=abc