Download Geometry Honors Section 9.3 Arcs and Inscribed Angles

Geometry Section 10.3
Inscribed Angles
Recall that a *central angle is an angle
whose vertex is at the center of the
circle and whose sides are radii.
What is the relationship between a
central angle and the are that it cuts
off?
The measure of the central angle
equals the measure of its
intercepted arc.
An *inscribed angle is an angle
whose vertex lies on the circle and
whose sides are chords.
By doing the following activity, you will be able to determine the relationship
between the measure of an inscribed angle and the measure of its
intercepted arc.
Given the measure of1 , complete the table.
Remember that the radii of a circle are congruent.
What does the table show about the
relationship between m1 and mPK ?
1
m1 
mPK
2
Inscribed Angle Theorem
If an angle is an inscribed angle,
the measure of the angle is equal
to ½ the intercepted arc.
Find the value of x in each figure. Q is the
center of each circle.
This work suggests the following theorem.
Theorem 10.11:
If a quadrilateral is inscribed in a
circle (i.e. its vertices lie on the
circle) then, its opposite angles are
supplementary.