http://www.ck12.org Chapter 9. Circles
- Draw central angles^6 DABand^6 CAE. Use colored pencils, if desired.
- Using your protractor, findm^6 DPB,m^6 DAB, andm^6 CAE. What ismDB̂andmCÊ?
- FindmDB̂+ 2 mCÊ.
- What do you notice?
Theorem 9-12:The measure of the angle formed by two chords that intersectinsidea circle is the average of the
measure of the intercepted arcs.
Inthepicturetotheleft:
m^6 SV R=1
2
(
m̂SR+mT Q̂)
=
mSR̂+mT Q̂
2=m^6 T V Qm^6 SV T=1
2
(
mST̂+mRQ̂)
=
mST̂+mRQ̂
2
=m^6 RV QThe proof of this theorem is in the review exercises.
Example 3:Findx.
a)