The Circle
ICSE Class 6 · Mathematics · Chapter 29
What this chapter covers
- What is a circle?
- Centre, radius and diameter
- Chord, arc and circumference
- Sector, segment and semicircle
- Interior and exterior of a circle
- Construction of a circle
Key points
- A circle is a closed curve in which every point is the same distance from a fixed point called the centre.
- A radius joins the centre to a point on the circle; all radii of a circle are equal.
- A diameter passes through the centre with both ends on the circle; diameter = 2 × radius.
- A chord joins any two points on a circle; the diameter is the longest chord.
- An arc is a part of the circle between two points on it.
- The circumference is the length once round the circle.
- A sector is enclosed by two radii and an arc; a segment is enclosed by a chord and an arc.
- A semicircle is half a circle, cut off by a diameter.
- Points closer to the centre than the radius are in the interior; points farther away are in the exterior.
- A circle is drawn with compasses opened to the radius, with the metal point fixed at the centre.
Questions answered
Name three things at home that have a circular edge.
A steel plate, a bangle and a coin. (A clock face, a bucket rim or a roti are also correct.)
The radius of a circle is 6 cm. What is its diameter?
2 × 6 cm = 12 cm.
The diameter of a wheel is 50 cm. What is its radius?
50 cm ÷ 2 = 25 cm.
Is every diameter a chord? Is every chord a diameter?
Every diameter is a chord, because both its end points are on the circle. A chord is a diameter only if it passes through the centre, so not every chord is a diameter.
Which is the longest chord of a circle?
The diameter.
A slice of a round cake has two straight edges that meet at the centre and a curved edge. Is it a sector or a segment?
It is a sector, because it is enclosed by two radii and an arc.
A circle has a radius of 5 cm. Point P is 7 cm from the centre. Where does P lie?
In the exterior, because 7 cm is more than the radius of 5 cm.
You must draw a circle of diameter 8 cm. How far apart should you open the compasses?
4 cm, which is the radius.