My Math Forum  

Go Back   My Math Forum > High School Math Forum > Geometry

Geometry Geometry Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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.
Haton Val is offline  
 
June 25th, 2017, 03:41 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 17,466
Thanks: 1312

Does this help?
skipjack is online now  
June 25th, 2017, 05:44 AM   #3
Newbie
 
Joined: Jun 2017
From: Viet Nam

Posts: 2
Thanks: 0

Quote:
Originally Posted by skipjack View Post
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.
Haton Val is offline  
June 26th, 2017, 01:36 AM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 17,466
Thanks: 1312

Are you given that $AB = AC$?

Did you try to prove the generalization given at the end of the linked page?
skipjack is online now  
Reply

  My Math Forum > High School Math Forum > Geometry

Tags
geometry



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Two 3-D Trigo Geometry Problems without using vector or coordinate geometry whsvin Geometry 0 February 1st, 2017 08:07 AM
Geometry help Ryan_aus Geometry 1 January 13th, 2014 06:24 AM
Coxeter's “Geometry Revisited” vs. “Introduction to Geometry becko Math Books 2 December 29th, 2010 09:47 PM
geometry arshakus Geometry 0 October 31st, 2010 05:25 AM
Use of plane geometry in coordinate geometry problems cursed_mask Geometry 0 July 22nd, 2008 11:52 PM





Copyright © 2017 My Math Forum. All rights reserved.