9.5. Inscribed Angles in Circles http://www.ck12.org
13.
- 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. - 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
- Inscribed^6 ABCand diameterBD
m^6 ABE=x◦andm^6 CBE=y◦
2.x◦+y◦=m^6 ABC - All radii are congruent
- 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◦ - Arc Addition Postulate
9.mAĈ= 2 x◦+ 2 y◦ - Distributive PoE
11.mAĈ= 2 m^6 ABC
12.m^6 ABC=^12 mAĈ