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Statement-1: Apoorv, standing on the
ground wants to observe the angle $α$ of elevation of the
top of a tower in front of him. He walks half the distance
towards the foot of the tower and finds the angle of elevation
is $π / 4$ . He observes $α = \tan^{- 1} (1 / 2)$
Statement-2: If the angles of elevation of the top of a tower
at three distinct points on the ground is $α$ , the points lie on
a circle with centre at the foot of the tower.

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STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for
STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is False

STATEMENT-1 is False, STATEMENT-2 is True

answer is B.

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Detailed Solution

Statement-2 is True, because if $h$ is the height
of the tower, the points are at a distance of $h \cot α$ from the
foot of the tower and hence lie on a circle. In statement-1,

if $h$ is the height of the tower then $h \cot α = 2 h \cot π / 4 =$

$2 h \Rightarrow α = \tan^{- 1} 1 / 2$

$\Rightarrow$ Statement-1 is true but does not follow from statement-2.

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