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 June 25th, 2017, 12:54 AM #1 Newbie   Joined: Jun 2017 From: Viet Nam Posts: 2 Thanks: 0 Geometry In a triangle $ABC\!$, let $A_0$ be the point where the interior angle bisector of angle $A$ meets with side $BC\!$. Similarly define $B_0$ and $C_0$. Prove that $\angle B_0A_0C_0 = 90^\circ$ if and only if $\angle BAC = 120^\circ\!$. p/s: please help me. I have posted this in many forums, but get no answer. Source: 2017 Math Majors of America Tournament for High Schools Tiebreaker Round problem 4. Last edited by skipjack; June 25th, 2017 at 03:55 AM.
 June 25th, 2017, 03:41 AM #2 Global Moderator   Joined: Dec 2006 Posts: 18,951 Thanks: 1599 Does this help?
June 25th, 2017, 05:44 AM   #3
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Joined: Jun 2017
From: Viet Nam

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Quote:
 Originally Posted by skipjack Does this help?
'This means that each step in the proof must use either a definition that is IF AND ONLY IF or a theorem that is IF AND ONLY IF. ... To prove a theorem of the form A IF AND ONLY IF B, you first prove IF A THEN B, then you prove IF B THEN A, and that's enough to complete the proof.;

That solution just proves 1 side, I mean how to prove the other side.

Last edited by skipjack; June 25th, 2017 at 07:23 AM.

 June 26th, 2017, 01:36 AM #4 Global Moderator   Joined: Dec 2006 Posts: 18,951 Thanks: 1599 Are you given that $AB = AC$? Did you try to prove the generalization given at the end of the linked page?

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