Inequality with Circle and Triangle in Euclidean Geometry

[seniorhs9]

Homework Statement

Please see below...

Homework Equations

Please see below...

The Attempt at a Solution

Hi. This question is on geometry with circle and triangle. I am stuck only on 2 parts of the solution and not the whole solution...

Thank you...

http://img256.imageshack.us/img256/9475/gtewp249no24.jpg

[ How did they get this? They never explained or proved this and it is NOT obvious from the picture.

Blue: How is that implication true? By what theorem or reasoning?

 

[TopCat]

To see that the red statement is true, observe that $\angle$ADO = $\angle$CDB > $\angle$BOD by Euclid I.32 (book I proposition 32).

In fact, that statement is superfluous. Once you know that $\angle$ADO > $\angle$BDO = $\angle$ADC = $\angle$AOD + $\angle$OAD, you know that $\angle$ADO > $\angle$OAD, and by Euclid I.19, OA > OD.