Circle Vocabulary and Properties
Grade 3Parts of a circle
You need precise vocabulary before tackling circle theorems. A radius runs from the centre to any point on the circumference. A diameter passes through the centre — it is twice the radius. A chord connects two points on the circumference without passing through the centre. An arc is a piece of the circumference. A sector is a pie-slice region bounded by two radii and an arc. A segment is the region between a chord and an arc.
A tangent touches the circle at exactly one point and is perpendicular to the radius at that point — that right angle is a key property in many questions.
Key property: tangent and radius
A tangent to a circle is always perpendicular to the radius drawn to the point of contact. This gives you a right angle to work with — use Pythagoras or trigonometry from there.
Worked example
EXAMPLE
A tangent from external point T touches a circle of radius 5 cm at point P. The distance from T to the centre O is 13 cm. Find the length TP.
Angle OPT = 90° (tangent perpendicular to radius). By Pythagoras: TP² = OT² − OP² = 13² − 5² = 169 − 25 = 144. TP = √144 = 12 cm.
