9.8. Angles Outside a Circle http://www.ck12.org
9.8 Angles Outside a Circle
Here you’ll learn how to calculate angles formed outside a circle by tangent and secant lines.
What if you wanted to figure out the angle at which the sun’s rays hit the earth? The sun’s rays hit the earth such
that the tangent rays determine when daytime and night time are. The time and Earth’s rotation determine when
certain locations have sun. If the arc that is exposed to sunlight is 178◦, what is the angle at which the sun’s rays hit
the earth(x◦)? After completing this Concept, you’ll be able to use properties of angles created by tangent lines to
answer this question.
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52416CK-12 Foundation: Chapter9AnglesOutsideaCircleA
Learn more about secants by watching the second half of this video.
Guidance
An angle is considered to be outside a circle if the vertex of the angle is outside the circle and the sides are tangents
or secants. There are three types of angles that are outside a circle: an angle formed by two tangents, an angle
formed by a tangent and a secant, and an angle formed by two secants. Just like an angle inside or on a circle, an
angle outside a circle has a specific formula, involving the intercepted arcs.
Investigation: Find the Measure of an Angle outside a Circle
Tools Needed: pencil, paper, ruler, compass, protractor, colored pencils (optional)
- Draw three circles and label the centersA,B, andC. In
⊙
Adraw two secant rays with the same endpoint,−→
DE
and−→
DF. In⊙
B, draw two tangent rays with the same endpoint,−→
LMand−→
LN. In⊙
C, draw a tangent ray and
a secant ray with the same endpoint,−→
QRand−→
QS. Label the points of intersection with the circles like they are
in the pictures below.