Playing with Constructions

Drawing circles with a compass, the radius and diameter, and constructing rectangles and squares with their sides and diagonals.

Key ideas

Every point on a circle is the same distance from its centre: that distance is the radius.
The diameter passes through the centre and is twice the radius.
Use the compass to copy a length exactly and to mark points at a given distance.
A rectangle has opposite sides equal, all angles 90°, and equal diagonals.
A square has all sides equal and all angles 90°; its diagonals are equal and cross at right angles.

Remember

Diameter	d = 2 × r
Rectangle	opposite sides equal; diagonals equal
Square	all sides equal; diagonals equal and perpendicular

Watch out

Using the diameter as the compass width.
Letting the compass slip, so the radius changes while drawing.
Drawing a corner that is not exactly 90° by eye.

Worked example

Vikram draws a square of side 12 cm and then a circle with its centre at one corner and radius 12 cm. How many corners of the square lie on the circle? How long is the diameter of the circle?

Working: the two corners next to the centre are 12 cm away; the far corner is farther

Answer: 2 corners; 24 cm