CK-12 Geometry Concepts

9.5. Inscribed Angles in Circles http://www.ck12.org

13.

14. Suppose thatABis a diameter of a circle centered atO, andCis any other point on the circle. Draw the line
    throughOthat is parallel toAC, and letDbe the point where it meetsBĈ. Explain whyDis the midpoint of
    BĈ.


15. Fill in the blanks of the Inscribed Angle Theorem proof.

Given: Inscribed^6 ABCand diameterBD

Prove:m^6 ABC=^12 mAĈ

TABLE9.2:

Statement Reason

1. Inscribed^6 ABCand diameterBD
   m^6 ABE=x◦andm^6 CBE=y◦
   2.x◦+y◦=m^6 ABC


2. All radii are congruent


3. Definition of an isosceles triangle
   5.m^6 EAB=x◦andm^6 ECB=y◦
   6.m^6 AED= 2 x◦andm^6 CED= 2 y◦
   7.mAD̂= 2 x◦andmDĈ= 2 y◦


4. Arc Addition Postulate
   9.mAĈ= 2 x◦+ 2 y◦


5. Distributive PoE
   11.mAĈ= 2 m^6 ABC
   12.m^6 ABC=^12 mAĈ