Circles

Basic vocabulary

History of the Circle• The circle has been known since before the

beginning of recorded history. It is the basis for the wheel, which, with related inventions such as gears, makes much of modern civilization possible. In mathematics, the study of the circle has helped inspire the development of geometry and calculus.

• Early science, particularly geometry and Astrology and astronomy, was connected to the divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles.

What is a circle?

• A circle is a locus of a point in a plane which moves such that its distance from a fixed point in the same plane remains constant.

• The fixed point is called the center of the circle and the fixed distance is called the radius.

O

Here O is the center and OP is the radius.

Naming a Circle

centerF

Use the center to name a circle.

Circle F

F

Parts of a Circle

Segments & Lines

chord

diameter

radius

tangent secant

Let’s review• The distance across a circle through

the center is called the diameter.• Radius: is the distance from the

center to any point on the circle. It is half the diameter.

• Chord: A line segment linking any two points on a circle

• Tangent: A line passing a circle and touching it at just one point.

• Secant: A line that intersects a circle at two points.

Formulas

• Radius/diameter

• Area

• Circumference

r = 1/2d and d=2r

C = 2∏r or C = ∏d

A = ∏r2

Types of Arcs

P

M

O

major arc

minor arc

semicircle N

MO

MNO

MON

Types of Angles

Central angle- Vertex is on the center.

Inscribed angle- Vertex is on the circle.

Circle folding activity

Measure of Arcs & Anglesminor arc = its central angle

major arc = 360 - its central angle

68°

68°

360 – 68 = 292

292°

Measure of Arcs & Anglesminor arc = its central angle

major arc = 360 - its central angle

semicircle = 180

180°

Measure of Arcs & Anglesminor arc = its central angle

major arc = 360 - its central angle

semicircle = 180

inscribed angle = ½minor arc

68°34°

SECTOR

Corresponding to a given arc, the

region bounded by the two radii and the arc itself.