# Circle Geometry - Direct Proofs

• Jul 27th 2009, 10:30 PM
Jimbolee
Circle Geometry - Direct Proofs
Hi I need help on these 2 questions, I have no clue what to do.

http://s2.lookpic.com/i/904/eYp6k37s.png
• Jul 27th 2009, 11:09 PM
red_dog
1) Let O be the center of the circle. Then the triangle ODA and ODC are congruent (because OD=OD, OA=OC and angles ODA and ODC are right). Therefore AD=DC.
Then the height BD is also median and that happens in an isosceles triangle.
• Jul 27th 2009, 11:12 PM
red_dog
2)
AC also bisects the arc BD. Then $\widehat{BEC}=\widehat{CED}$ But $\widehat{BEC}+\widehat{CED}=180\Rightarrow \widehat{BEC}=\widehat{CED}=90$