☰ Contents · Geometry

Circle and disc. Practical measuring

Lessons 7–8 · 2 lessons · Geometry Grade 7, corrected and expanded 3rd edition. Yangiyo‘l Poligraf Servis, Tashkent, 2017 (approved by the Ministry of Public Education)
7

Circle and disc

Textbook: pp. 18–19
GoalKnow the circle, the disc and their elements.
New words
circle (the curve) · aylanacentre · markazradius · radiuschord and diameter · vatar va diametr
Explanation

The set of all points that satisfy the same condition is called a locus of points. For example, a circle is the set of all points of the plane lying at the same distance from a chosen point O; O is the centre of the circle. The distance from any point of the circle to the centre is the radius; a segment joining two points of the circle is a chord; a chord through the centre is a diameter, and it is the longest chord. A diameter consists of two radii, so d = 2r. The part of the plane bounded by a circle is called a disc. We draw circles with a compass; its point is sharp, so use it carefully and under an adult’s supervision.

Worked examples
If a circle’s radius is 7 cm, its diameter is 7 · 2 = 14 cm.
In a disc with centre O and radius 5 cm, point A with OA = 3 cm is inside, B with OB = 5 cm is on the circle, and C with OC = 6 cm is outside.
Class activity

“Rope circle”: one pupil stands at the centre, another walks around at the length of a rope. How does the circle appear? (Only in a safe, flat place.)

Practice
1
A circle has radius 12 cm. Find its diameter (cm).
2
A disc has diameter 38 cm. What is its radius (cm)?
3
What is the longest chord of a circle of radius 10 cm (cm)?
4
Why is a diameter the longest chord?