Q.

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
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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=