Properties of Circles

What you'll learn

Identify radii, chords, tangents, and central angles
Relate arc measures to central and inscribed angles
Find arc length and sector area

Words to know

Radius —: a segment from the center to the circle
Chord —: a segment joining two points on the circle
Tangent —: a line that touches the circle at exactly one point
Central angle —: an angle with its vertex at the center
Arc —: part of the circle between two points

Why it matters Circle properties describe wheels, gears, clocks, and satellite orbits, wherever motion turns around a center.

Worked examples

Model ItI do

Name the radius, the chord, and the tangent shown in circle O.

The segment from center O to the edge is the radius r. The segment joining two points on the circle is the chord. The line touching the circle at just one point is the tangent.

Try It TogetherWe do

A central angle of 90 degrees sits in a circle. What is the measure of the arc it cuts off?

A central angle has the same measure as its intercepted arc. So the arc measures 90 degrees.

Now YouYou do

An inscribed angle intercepts an arc of 100 degrees. Find the inscribed angle's measure.

An inscribed angle is half its intercepted arc. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

1.A segment from the center of a circle to a point on the circle is called a _____.
2.A central angle of 80 degrees cuts off an arc of how many degrees?
3.A line that touches a circle at exactly one point is a _____.

On Level

The core Quick Check from the book.

1.A segment from the center to the circle is called a _____.
2.A line touching a circle at one point is a _____.
3.A central angle of 70 degrees cuts off an arc of how many degrees?
4.An inscribed angle intercepts a 60 degree arc. Find the angle.
5.How many degrees are in a full circle?

Challenge

Stretch your thinking.

1.An inscribed angle intercepts an arc of 140 degrees. Find the inscribed angle's measure.
2.An inscribed angle measures 35 degrees. Find the measure of its intercepted arc.
3.An angle is inscribed in a semicircle, so its intercepted arc is 180 degrees. Find the angle.