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Subject: "ABC triangle"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #386
Reading Topic #386
Anderson derty
guest
 Apr-23-09, 08:19 PM (EST)
 
"ABC triangle"
 
   ABC triangle BD bisects ∠ABC, D on AC, m∠ABC =80 , AD=BD+BC find m∠C


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  Subject     Author     Message Date     ID  
  RE: ABC triangle alexbadmin Apr-24-09 1
     RE: ABC triangle Anderson derty Apr-24-09 2
         RE: ABC triangle alexbadmin Apr-24-09 3
             RE: ABC triangle Anderson derty Apr-24-09 4
                 RE: ABC triangle alexbadmin Apr-24-09 5
                 RE: ABC triangle jvriens Jul-14-11 6
                     RE: ABC triangle alexbadmin Jul-15-11 7
                         RE: ABC triangle mfernanj Jul-15-11 8
                             RE: ABC triangle alexbadmin Jul-15-11 9
                                 RE: ABC triangle alexbadmin Jul-15-11 10
                                     RE: ABC triangle alexbadmin Jul-15-11 11
                                         RE: ABC triangle jvriens Jul-24-11 12
                                             RE: ABC triangle alexbadmin Jul-24-11 13

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alexbadmin
Charter Member
2815 posts		 Apr-24-09, 00:12 AM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
1. "RE: ABC triangle"
In response to message #0
 
   Another 80°, of course. Why do you ask?


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Anderson derty
guest
 Apr-24-09, 12:49 PM (EST)
 
2. "RE: ABC triangle"
In response to message #1
 
   ok I know its =80 but how I can prove these


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alexbadmin
Charter Member
2815 posts		 Apr-24-09, 12:52 PM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
3. "RE: ABC triangle"
In response to message #2
 
   >ok I know its =80 but how I can prove these

You'll have to tell me

1. how do you know it's 80°,
2. where did the problem come from.

(I'd appreciate some detail. E.g., if it came from a textbook, which one it was, which section - the more the better.)

OK? Thank you.


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Anderson derty
guest
 Apr-24-09, 04:03 PM (EST)
 
4. "RE: ABC triangle"
In response to message #3
 
   >ok I know its =80 but how I can prove these

You'll have to tell me

1. how do you know it's 80°,
2. where did the problem come from.

(I'd appreciate some detail. E.g., if it came from a textbook, which one it was, which section - the more the better.)

OK? Thank you.

https://www.artofproblemsolving.com/Forum/viewtopic.php?t=267181


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alexbadmin
Charter Member
2815 posts		 Apr-24-09, 08:57 PM (EST)
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5. "RE: ABC triangle"
In response to message #4
 
   Once you know that the angle C is 80°, the rest is simple.

Observe that small rotations of AC around D move AD and BC in opposite directions: when AD increases, BC decreases and vice versa. BD of course remains fixed. This tells you that if, for C = 80° you have AD = BC + BD, you can't have this equality anywhere near 80°. Moving away makes it even worse.


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jvriens
Member since Aug-27-03
 Jul-14-11, 01:39 PM (EST)
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6. "RE: ABC triangle"
In response to message #4
 
   The drawing is clearly and speaks for itself, but how can the proof be
delivered by logical deduction, possibly using the drawing ?


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alexbadmin
Charter Member
2815 posts		 Jul-15-11, 02:54 AM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
7. "RE: ABC triangle"
In response to message #6
 
   I placed a solution at

https://www.cut-the-knot.org/triangle/80-80-20/Partition3Sol.shtml


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mfernanj
Member since Jul-15-11
 Jul-15-11, 04:17 PM (EST)
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8. "RE: ABC triangle"
In response to message #7
 
   >I placed a solution at
>
>https://www.cut-the-knot.org/triangle/80-80-20/Partition3Sol.shtml

Why CD=DF?


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alexbadmin
Charter Member
2815 posts		 Jul-15-11, 04:19 PM (EST)
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9. "RE: ABC triangle"
In response to message #8
 
   Because CD = BF and BF = DF.


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alexbadmin
Charter Member
2815 posts		 Jul-15-11, 05:04 PM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
10. "RE: ABC triangle"
In response to message #9
 
   Oops, and why CD = BF? Must think of that. Sorry.


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alexbadmin
Charter Member
2815 posts		 Jul-15-11, 06:01 PM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
11. "RE: ABC triangle"
In response to message #10
 
   Here's a corrected one:

https://www.cut-the-knot.org/triangle/80-80-20/Partition3SolC.shtml


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jvriens
Member since Aug-27-03
 Jul-24-11, 06:40 AM (EST)
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12. "RE: ABC triangle"
In response to message #11
 
   Using twice the sine rule , I got the following ( difficult ) formula:

(sin(40)- sin(100-x))/(sin(100-x))= (sin(140-x))/(sin(x))

(the formula is correct if x= 80, x= angle ACB).

But,so far, I have had no success trying to solve this formula.


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alexbadmin
Charter Member
2815 posts		 Jul-24-11, 03:04 PM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
13. "RE: ABC triangle"
In response to message #12
 
   It's unfortunate. I do not see how to simplify it.


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