Question

Draw a circle and any two of its diameters. If you join the ends of these diameters, what is the figure obtained? What figure is obtained, if the diameters are perpendicular to each other? How do you check your answer?

Answer 1

Draw a circle with radius 2.5 cm with the help of compass.

(i) By joining the ends of two diameters, we get a rectangle.
For example in the figure below we find AB = CD = 4 cm, BC = AD = 3 cm, i.e. pairs of opposite sides are equal and also $\angle A=\angle B=\angle C=\angle D={90}^{\circ }$, i.e. each angle is of 90. Hence, it is a rectangle.

(ii) If the diameters are perpendicular to each other, then by joining the ends of two diameters, we get a square. By measuring, we find that AB = BC = CD = DA = 3.5 cm (approx.), i.e. all four sides are equal. Also $\angle A=\angle B=\angle C=\angle D={90}^{\circ }$, i.e. each angle is of 90. Hence, it is a square.