Question

Draw a circle of any radius, say $4cm$. Draw any two of its diameters. Join the ends of these diameters. What figure do you obtain? What figure is obtained if the diameters are perpendicular to each other?

Answer 1

Step 1: Construction of circle

1. Open the compasses for the required radius, i.e.,$4cm$ , by putting the steel point on fixed point say $C$ and opening the pencil upto $4cm$.

2. Mark point $C$ as the centre of the circle.

3. Keeping steel point fixed at $C$, swing the pencil leg of the compasses around to draw a circle of radius $4cm$.

Step 2: Construction of diameters

1.Draw a line segment $AB$ passing through the centre $C$ of the circle and with its end points lying on the circle. This is the diameter of the circle.

2. Draw one more such diameter at any angle to the previous one and label it as $DE$.

3. Join the ends of these diameters i.e. join $A\to D\to B\to E\to A$ using straight lines.

Hence, we see that $ADBE$ is a rectangle as all the angles are right angles but adjacent sides are unequal.

Step 3: Construction of perpendicular diameters

1.Draw one diameter $AB$ as above.

2. Put protractor at $AB$ with centre at $C$ and mark $90°$ mark on the circle and marks as $D$.

3. From $D$ draw diameter of the circle as before. Hence, we get two perpendicular diameters.

4. Join the ends of these diameters i.e. join $A\to D\to B\to E\to A$ using straight lines.

Hence, here we see that $ADBE$ is a square as all the angles are right angles and all sides are equal.