10.6 More Angle Arc Theorems

After studying this section, you will be able to recognize congruent inscribed and tangent-chord angles; determine the measure of an angle inscribed in a semicircle and apply the

relationship between the measures of a tangent-tangent angles and its minor arc..

Theorem If two inscribed or tangent chord angles intercept the same arc, then they are congruent.

A

B

O

D

C

O

E

Theorem If two inscribed or tangent-chord angles intercept congruent arcs, then they are congruent.

Theorem An angle inscribed in a semicircle is a right angle.

A

C

B

Theorem The sum of the measures of a tangent-tangent angle and its minor arc is 180.

E

F

D

O

130

Minor arc DE = 130 find the measure of angle F.

Example 1N

L

O

S

V

Given circle O

Conclusions

Triangle LVE is similar to triangle NSE

E

Example 2

In circle O, segment BC is a diameter and the radius of the circle is 20.5 mm. Chord AC has a length of 40 mm. Find AB.

A

BO

C

Example 3

Given: circle O with tangent at B

A B

D

O

CAB�������������� �

AB CD���������������������������������������� ���

Prove: C BDC

Summary

Summarize what you have learned in this lesson.

Homework: worksheet