Circles
9 flashcards to master Circles
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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.
About Circles (4.6)
These 9 flashcards cover everything you need to know about Circles for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.
What You'll Learn
- 6 Definitions - Key terms and their precise meanings that examiners expect
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Continue Learning
After mastering Circles, explore these related topics:
- 4.5 Quadrilaterals - 9 flashcards
- 4.7 Circle theorems - 9 flashcards
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