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Inequality with Circle and Triangle in Euclidean Geometry

  • Thread starter seniorhs9
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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 [Broken]

[ 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?
 
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Answers and Replies

  • #2
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To see that the red statement is true, observe that [itex]\angle[/itex]ADO = [itex]\angle[/itex]CDB > [itex]\angle[/itex]BOD by Euclid I.32 (book I proposition 32).

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

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