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Statement $- 1$ : Three poles of height $a, b, c$ stand at the points $A, B, C$ respectively and subtend the same angle $α$ at a point $O$ on the horizontal line through the feet of the poles. If $a, b, c$ are in A.P., then $A B = B C .$
Statement $- 2$ : $O$ is the centre of a circular field and $A$ is any point on its boundary. Two poles standing at $A$ and $O$ subtend the same angle $α$ at a point $B$ on the other end of the diameter through $A .$ Height of the pole at $A$ is twice the height of the plot at $O .$

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

STATEMENT-1 is False, STATEMENT-2 is True

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

STATEMENT-1 is True, STATEMENT-2 is False

answer is B.

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Detailed Solution

$\begin{array}{l} A B = O A - O B = (a - b) \cot α \\ B C = O B - O C = (b - c) \cot α \\ \Rightarrow A B = B C \end{array}$

$[∵ a, b, c$ are in A.P. $\Rightarrow b - a = c - b]$

$\Rightarrow$ Statement $- 1$ is True.

In statement $- 2$ if r is the radius of the circular field, then $O B = r, A B = 2 r$

Height of the pole at $A = 2 r \tan a = 2 x$ height of the pole at $O .$

$\Rightarrow$ Statement $- 2$ is also correct but does not lead to statement $- 1 .$

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