Circles
Cambridge IGCSE Mathematics (0580) · Unit 4: Geometry · 9 flashcards
Circles is topic 4.6 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 4 — Geometry , alongside Angles, Angles in polygons and Parallel lines. In one line: The radius is the distance from the center of the circle to any point on its circumference. The diameter is twice the length of the radius (d = 2r).
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.
The deck below contains 9 flashcards — 6 definitions — covering the precise wording mark schemes reward. Use the 6 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
The radius of a circle and how it relates to the diameter
The radius is the distance from the center of the circle to any point on its circumference. The diameter is twice the length of the radius (d = 2r).
Define the radius of a circle and how it relates to the diameter.
The radius is the distance from the center of the circle to any point on its circumference. The diameter is twice the length of the radius (d = 2r).
A circle has a diameter of 14 cm. Calculate its circumference, leaving your answer in terms of π.
Circumference (C) = πd. Given d = 14 cm, C = 14π cm.
Explain what a chord is and how it differs from a diameter.
A chord is a line segment that connects two points on a circle's circumference. A diameter is a special chord that passes through the center of the circle and is the longest possible chord.
Define an arc of a circle and differentiate between a minor arc and a major arc.
An arc is a portion of the circumference of a circle. A minor arc is shorter than half the circumference, while a major arc is longer.
Describe what a sector of a circle is and give the formula to calculate its area.
A sector is the region enclosed by two radii and the arc they subtend. The area of a sector is (θ/360)πr², where θ is the central angle in degrees and r is the radius.
Explain what a segment of a circle is and how it differs from a sector.
A segment is the region enclosed by a chord and the arc it subtends. Unlike a sector, it is not bounded by two radii, but by a chord.
Define a tangent to a circle and state its relationship to the radius at the point of tangency.
A tangent is a line that touches the circle at only one point. The tangent is perpendicular to the radius drawn to the point of tangency, forming a 90-degree angle.
The area of a circle is 25π cm². Find the length of its radius.
Area (A) = πr². Given A = 25π, πr² = 25π. Therefore, r² = 25, and the radius r = 5 cm.
A chord of length 16 cm is 6 cm from the center of a circle. Calculate the radius of the circle.
Draw a right-angled triangle from the center to the midpoint of the chord. Use Pythagoras theorem: r² = 6² + (16/2)². Therefore r² = 36 + 64 = 100, so r = 10 cm.
Key Questions: Circles
Define the radius of a circle and how it relates to the diameter.
The radius is the distance from the center of the circle to any point on its circumference. The diameter is twice the length of the radius (d = 2r).
Explain what a chord is and how it differs from a diameter.
A chord is a line segment that connects two points on a circle's circumference. A diameter is a special chord that passes through the center of the circle and is the longest possible chord.
Define an arc of a circle and differentiate between a minor arc and a major arc.
An arc is a portion of the circumference of a circle. A minor arc is shorter than half the circumference, while a major arc is longer.
Describe what a sector of a circle is and give the formula to calculate its area.
A sector is the region enclosed by two radii and the arc they subtend. The area of a sector is (θ/360)πr², where θ is the central angle in degrees and r is the radius.
Explain what a segment of a circle is and how it differs from a sector.
A segment is the region enclosed by a chord and the arc it subtends. Unlike a sector, it is not bounded by two radii, but by a chord.
Tips to avoid common mistakes in Circles
- ● Remember the angle at the center links to the circumference: sector area is a fraction of πr², while arc length is a fraction of 2πr.
- ● Get comfortable using the dedicated 'pi' button on your calculator for the most accurate value during calculations.
More topics in Unit 4 — Geometry
Circles sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
10 flashcards
9 flashcards
10 flashcards
10 flashcards
9 flashcards
9 flashcards
9 flashcards
9 flashcards
9 flashcards
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Circles deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
How to study this Circles deck
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