Question

Four poles are to be erected in a garden such that two poles form a line segment and the other two poles, lying on the same side of the line segment, are subtended at equal angles from the line segment. With the mentioned condition, the four poles can lie on a -

• A. square
• B. rectangle
• C. circle

Answer 1

Answer: (A), (B), (C)

circle

We know that if the line segment joining two points subtends equal angles at two other points lying on the same side of the line, then all the four points lie on a circle.


Here, poles C and B form a line segment.
The other two poles A and D lie on the same side of the line segment CB.
Given: $\angle D=\angle A$
$\therefore$ All the four poles must lie on a circle.

However, when the four poles are at the vertices of a square or a rectangle, the given condition is also satisfied.

Hence, all the given options are correct.