Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inequality with Circle and Triangle in Euclidean Geometry

  1. Nov 26, 2011 #1
    1. The problem statement, all variables and given/known data

    Please see below...

    2. Relevant equations

    Please see below...

    3. 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?
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Nov 29, 2011 #2
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook