Define a chord of a circle.

A chord is a straight line joining two points on the circumference. It does not have to pass through the centre, and it does not extend beyond the circle.

Define a segment of a circle.

A segment is the region enclosed between a chord and the arc that the chord cuts off. Every chord creates two segments, a larger one and a smaller one.

Define a tangent to a circle.

A tangent is a straight line that touches the circumference at exactly one point . Unlike a chord, it does not cut across the circle at all.

True or False? Every diameter is also a chord.

True. A diameter joins two points on the circumference, which is exactly what a chord does. A diameter is simply the special chord that passes through the centre , and it is the longest chord a circle has.

Why is a diameter a line of symmetry of a circle?

Because it passes through the centre , so it splits the circle into two identical halves. A circle has infinitely many lines of symmetry, since every diameter is one.

What angle does a tangent make with the radius at the point where they meet?

A tangent and a radius meet at a right angle , so they are perpendicular at the point of contact.

Two tangents are drawn to a circle from the same point outside it. What do you know about their lengths?

The two tangents are equal in length , measured from the outside point to where each one touches the circle.

True or False? A line from the centre of a circle to the midpoint of a chord that is not a diameter meets the chord at right angles.

True. The line cuts the chord into two equal halves and is perpendicular to it.

How does a line from the centre that is perpendicular to a chord help you find the length of the chord?

The perpendicular line cuts the chord in half , making a right-angled triangle whose hypotenuse is a radius . Find half of the chord using Pythagoras or trigonometry, then double it.

True or False? A tangent is perpendicular to every chord that starts at the point where the tangent touches the circle.

False. The only chord from that point that meets the tangent at a right angle is the diameter , because it passes through the centre.

Why is a triangle formed by a chord and two radii always isosceles?

Because two of its sides are radii , and all radii of a circle are the same length. So the two angles at the ends of the chord are equal .

Two chords of the same circle are equal in length. What do you know about their distances from the centre?

Chords of equal length are equidistant from the centre, meaning they are the same distance from it.

Define the term radius of a circle .

A radius of a circle is the distance from the centre of a circle to its circumference .

True or False? Every point on the circumference of a circle is equidistant from its centre .

True. Every point on the circumference of a circle is equidistant from its centre .

What is the minor arc ?

The minor arc is the smaller of the two arcs created by two points on the circumference of a circle.

What is the major sector ?

The major sector is the larger of the two sectors created by two radii in a circle.

True or False? The area of a sector is a fraction of the area of the whole circle .

True. The area of a sector is a fraction of the area of the whole circle .

IGCSEMathsEdexcelMaths AFoundationFlashcards4. Geometry & TrigonometryCircles, Arcs & Sectors

Circles, Arcs & Sectors (Edexcel IGCSE Maths A: Foundation): Flashcards

Exam code: 4MA1

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FrontProperties of Circles
Define a chord of a circle.

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Cards in this collection (27)

Define a chord of a circle.
A chord is a straight line joining two points on the circumference.
It does not have to pass through the centre, and it does not extend beyond the circle.
Define a segment of a circle.
A segment is the region enclosed between a chord and the arc that the chord cuts off.
Every chord creates two segments, a larger one and a smaller one.
Define a tangent to a circle.
A tangent is a straight line that touches the circumference at exactly one point.
Unlike a chord, it does not cut across the circle at all.
True or False?
Every diameter is also a chord.
True.
A diameter joins two points on the circumference, which is exactly what a chord does.
A diameter is simply the special chord that passes through the centre, and it is the longest chord a circle has.
Why is a diameter a line of symmetry of a circle?
Because it passes through the centre, so it splits the circle into two identical halves.
A circle has infinitely many lines of symmetry, since every diameter is one.
What angle does a tangent make with the radius at the point where they meet?
A tangent and a radius meet at a right angle, so they are perpendicular at the point of contact.
Complete the circle theorem:
The perpendicular bisector of a $______$ always passes through the $______$ of the circle.
The completed theorem is:
The perpendicular bisector of a chord always passes through the centre of the circle.
Two tangents are drawn to a circle from the same point outside it. What do you know about their lengths?
The two tangents are equal in length, measured from the outside point to where each one touches the circle.
True or False?
A line from the centre of a circle to the midpoint of a chord that is not a diameter meets the chord at right angles.
True.
The line cuts the chord into two equal halves and is perpendicular to it.
How does a line from the centre that is perpendicular to a chord help you find the length of the chord?
The perpendicular line cuts the chord in half, making a right-angled triangle whose hypotenuse is a radius.
Find half of the chord using Pythagoras or trigonometry, then double it.
Tangents from a point $T$ touch a circle with centre $O$ at the points $R$ and $S$ . What shape is $O R T S$ , and which of its angles do you know?
The quadrilateral $O R T S$ is a kite with right angles at $R$ and $S$ , where each tangent meets a radius.
It splits into two congruent right-angled triangles, so Pythagoras and trigonometry can be used on them.
True or False?
A tangent is perpendicular to every chord that starts at the point where the tangent touches the circle.
False.
The only chord from that point that meets the tangent at a right angle is the diameter, because it passes through the centre.
Why is a triangle formed by a chord and two radii always isosceles?
Because two of its sides are radii, and all radii of a circle are the same length.
So the two angles at the ends of the chord are equal.
Two chords of the same circle are equal in length. What do you know about their distances from the centre?
Chords of equal length are equidistant from the centre, meaning they are the same distance from it.
What is the formula for the circumference of a circle?
There are two formulas for the circumference of a circle, $C = 2 π r = π d$
Where:
- $C =$ circumference
- $r =$ radius
- $d =$ diameter
Define the term radius of a circle.
A radius of a circle is the distance from the centre of a circle to its circumference.
True or False?
Pi ( $π$ ) is the ratio between a circle's diameter and its circumference.
True.
Pi ( $π$ ) is the ratio between a circle's diameter and its circumference.
What is the relationship between the diameter of a circle and the radius?
The diameter of a circle is twice the length of the radius ( $d = 2 r$ ).
True or False?
Every point on the circumference of a circle is equidistant from its centre.
True.
Every point on the circumference of a circle is equidistant from its centre.
What is an arc?
An arc is a part of the circumference of a circle.
What is the minor arc ?
The minor arc is the smaller of the two arcs created by two points on the circumference of a circle.
What is the formula for the length of an arc?
The formula for the length of an arc is $l = \frac{θ}{360} \times 2 π r$
Where:
- $l =$ length of the arc
- $θ =$ angle of the sector
- $r =$ radius
What is a sector?
A sector is the part of a circle enclosed by two radii and an arc.
What is the major sector?
The major sector is the larger of the two sectors created by two radii in a circle.
What is the formula for the area of a sector?
The formula for the area of a sector is $A = \frac{θ}{360} \times π r^{2}$
Where:
- $A =$ area
- $θ =$ the angle of the sector
- $r =$ radius
True or False?
The area of a sector is a fraction of the area of the whole circle.
True.
The area of a sector is a fraction of the area of the whole circle.
In the equation $A = \frac{θ}{360} \times π r^{2}$ , what does $θ$ represent?
In the equation $A = \frac{θ}{360} \times π r^{2}$ , the quantity $θ$ represents the angle of the sector.

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