Question

If a flag-staff subtends the same angle at the points A, B, C, D on the horizontal plane through the foot of the flag-staff, then A, B, C, D are the vertices of a

• A. square
• B. cyclic quadrilateral
• C. rectangle
• D. none of these

Answer 1

The correct option is B cyclic quadrilateral

h = $R_1$ tan $\theta$ = $R_2$ tan $\theta$ = $R_3$ tan $\theta$ = $R_4$ tan$\theta$
Above implies that $R_1=R_2=R_3=R_4$ i.e. the distances of the four points from the foot of the tower O are equal.
Thus $ABCD$ is a cyclic quadrilateral.