The Arc of a Circle

Inscribed and Tangent Angles

An Inscribed AngleAn angle with all three points on the

edges of a circle.

ABC is the inscribed angle.

The measure of the minor arc created by an inscribed angle is twice as large as the measure of the angle.

AC = 2(30°) = 60°

A

C

B

30°

Example with an Inscribed Angle

AC is the minor arc:It is twice the measure of the inscribed angle: 2(40) = 80°

A

C

B

AB = 110° AC =_____ABC = 40°

CB = _____

80°

170°

The sum of all the arcs is 360°AB + AC + BC = 360110 + 80 + x = 360

x = 170°

A line is tangent to a circle if it touches the circle at only one point.

Angle made by a chord and tangent line:

The measure of the arc is twice the measure of the angle.

A

B C

M

P

ABC = 75°

AMB = 2(75) = 150° APB = 360 – 150 = 210°