Properties of Circles
The properties of a circle are its key parts. The radius is the fixed distance from the centre to any point on the edge. The diameter goes through the centre, so it is twice the radius (a 16 cm diameter has an 8 cm radius).
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Properties of a Circle
- The diameter goes through the centre and is twice the radius.
- A sector is made from two radii and the arc between them.
- A tangent touches the circle at one point and is perpendicular to the radius.
Finding Points with Circles
- All points the same distance from a point lie on a circle, and that distance is the radius.
- The intersections of circles show the possible answers.
Practice Questions
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What is the constant distance from the centre of a circle to any point on its edge called?
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The radius is the constant distance from the centre to any point on the circle's edge.
What do we call a straight line that touches a circle at exactly one point?
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A tangent touches the circle at exactly one point and is perpendicular to the radius at that point.
What is the part of a circle enclosed by a chord and the arc above it called?
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A segment is the area enclosed by a chord and the arc above it.
A circle has a diameter of . What is its radius?
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The radius is half the diameter, so .
A tangent touches a circle at exactly one point. At this point, what is the angle between the tangent and the radius?
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A tangent is always perpendicular to the radius at the point of contact, forming a angle.
A circle has a radius of . What is the length of the longest chord in the circle?
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The diameter is the longest chord in a circle, and it is twice the radius: .
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Interactive Activity
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Students Also Ask
The questions students bump into most on this topic
The longest chord in a circle is the diameter. A chord joins two points on the circle with a straight line. The diameter is the special chord that passes through the centre. Passing through the centre is what makes the diameter the longest chord you can draw.
A sector is the pie slice shape between two radii and the arc joining them. So it always reaches the centre. A segment is the area between a chord and the arc above it. Its straight side is a chord, not two radii reaching the centre.
Yes. A tangent touches a circle at exactly one point. At that point, it meets the radius at a right angle (90°). This perpendicular relationship holds for every tangent you draw to a circle, whatever point on the edge it touches.
Yes. The diameter passes straight through the centre, and it is exactly two times the radius. So if you know the radius, double it to find the diameter. And if you know the diameter, halve it to get back to the radius.
Draw a circle around the first point, using that distance as the radius. Then draw a circle around the second point, using its distance. The two points where the circles cross are the correct distance from both points at once. Those are the points you need.
Circles appear in wheels. The even distance from the centre to the edge lets them roll smoothly, without bumping up and down. The two-circle method also locates a spot a set distance from two places. An example is a car park a fixed distance from two shopping centres.