GCSE · Maths · Edexcel · Spec 1MA1 · Foundation+Higher
Circle definitions and properties
Chord or diameter? Sector or segment? Two quick questions sort out every part of a circle.
Circles · Drag and watch
OA runs from the centre to the circumference, so it's a radius, and it's 5 cm wherever A goes. AB has both ends on the circumference, so it's a chord. Slide it through O and it becomes a diameter: two radii end to end, 10 cm. Angles APB and AOB are both subtended by chord AB, because their arms meet A and B.
Drag A or B round the circle. Radius OA always reads 5.0 cm. Chord AB changes length, and it is longest, 10.0 cm, when it passes through the centre O. Then drag P round the circle: the arms of angle APB always run to A and B.
Circles · Sort the parts
Length or area? Centre or not?
Pick a part, then pick where it belongs.
Is it a length inside the circle, a length on or outside the circle, or an area?
Still to sort
Length inside the circle (0)
A straight line drawn inside the circle
Where the line is: A chord and a tangent are both straight, but a chord's ends sit on the circle, so it lies inside. A tangent stays outside and just touches.
Length on or outside the circle (0)
Runs along the edge, or sits outside it
Area (0)
A region you could shade in
Where the line is: An arc is a length, the curved edge. A sector or a segment is the region inside that edge.
Each part of a circle is either a length (something you measure along) or an area (a region you could shade in). Sort all eight, then switch the question and sort them again by what they do with the centre.
Predict, then check
Tangents are about what the line WOULD do, not just what's drawn.
Line segment PT starts at P, outside a circle, and stops at T, on the circumference. As drawn, it meets the circle at T and nowhere else. But if you kept drawing past T, the line would head into the circle. Is PT a tangent?
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
Eight parts, two questions: length or area, and what it does with the centre.
What you need to know
- Radius: centre to circumference. Diameter: a chord through the centre, twice the radius.
- Chord: any straight line with both ends on the circumference. It doesn't have to pass through the centre.
- Circumference: the distance all the way round. Arc: part of the circumference.
- Tangent: meets the circle exactly once, even when it's extended into a full line.
- Sector: two radii and an arc. Segment: a chord and an arc. Minor is under 50% of the circle, major is over 50%.
- An angle is subtended by a chord or an arc when its two arms meet the chord's or arc's endpoints.
The big picture
A circle has eight named parts: radius, diameter, chord, circumference, arc, tangent, sector and segment. Six are lengths and two are areas. To name a part, look at where it touches the circle and whether it passes through, starts at or ignores the centre. A diameter is the chord through the centre, twice the radius. A semicircle counts as a sector and a segment at the same time.
Key points
Worked example
Problem
A circle has centre O and radius 6 cm. Points A, B and C lie on the circumference. Line AC passes through O, and line AB does not. (a) Name line AB. (b) Name line AC and find its length. (c) Name the region enclosed by OA, OB and the shorter arc AB.
⚠ Watch out
Calling any line across a circle a diameter. It's only a diameter if it passes through the centre. Otherwise it's a chord.
Memory hook
Think pizza. A sector is a normal slice: two straight cuts from the middle, plus crust. A segment is what you get with one straight cut across, missing the middle. Middle means sector. One cut means segment.
Check yourself
Without looking back: a line touches a circle at exactly one point. What else do you need to check before you can call it a tangent?
Flashcards
(12)What is a radius?
How long is a diameter compared with a radius?
What is a chord?
What is the circumference?
What is an arc?
What must be true for a line to be a tangent?
Which parts of a circle are areas?
What bounds a sector?
What bounds a segment?
What's the difference between 'minor' and 'major' for a sector or segment?
Why is a semicircle both a sector and a segment?
What does it mean for an angle to be subtended by a chord AB?
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
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Keep me postedMore Edexcel GCSE Maths topics
- Angle properties and parallel lines
- Area of any triangle (½ab sin C)
- Calculating with roots and indices
- Circumference, area of circle and 3D solids
- Conditional probability
- Estimation and approximation
- Geometrical problems on coordinate axes
- Gradients and areas under curves
- Gradients and intercepts of linear functions
- Iterative methods
- Limits of accuracy and bounds
- Measuring lines, angles and bearings
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