CK-12 Geometry Concepts

http://www.ck12.org Chapter 9. Circles

To finda, it is in line with 50◦and 45◦. The three angles add up to 180◦. 50◦+ 45 ◦+m^6 a= 180 ◦,m^6 a= 85 ◦.

bis an inscribed angle, so its measure is half ofmAĈ. From the Chord/Tangent Angle Theorem,mAĈ= 2 ·m^6 EAC=
2 · 45 ◦= 90 ◦.

m^6 b=^12 ·mAĈ=^12 · 90 ◦= 45 ◦.

To findc, you can either use the Triangle Sum Theorem or the Chord/Tangent Angle Theorem. We will use the
Triangle Sum Theorem. 85◦+ 45 ◦+m^6 c= 180 ◦,m^6 c= 50 ◦.

Watch this video for help with the Examples above.

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CK-12 Foundation: Chapter9AnglesOnandInsideaCircleB

Vocabulary

Acircleis the set of all points that are the same distance away from a specific point, called thecenter. Aradiusis
the distance from the center to the circle. Achordis a line segment whose endpoints are on a circle. Adiameteris
a chord that passes through the center of the circle. The length of a diameter is two times the length of a radius. A
central angleis the angle formed by two radii and whose vertex is at the center of the circle. Aninscribed angle
is an angle with its vertex on the circle and whose sides are chords. Theintercepted arcis the arc that is inside
the inscribed angle and whose endpoints are on the angle. Atangentis a line that intersects a circle in exactly one
point. Thepoint of tangencyis the point where the tangent line touches the circle.

Guided Practice

Findx.

Answers:

Use the Intersecting Chords Angle Theorem and write an equation.

1. The intercepted arcs forxare 129◦and 71◦.

x=

129 ◦+ 71 ◦

2

=

200 ◦

2

= 100 ◦

2. Here,xis one of the intercepted arcs for 40◦.

40 ◦=

52 ◦+x

2

80 ◦= 52 ◦+x

38 ◦=x