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. Let ABCD be a convex quadrilateral with AB = 11, BC = 7, CD = 11, DA = 26. If ∠BEC = 120◦ , where E is the point of intersection of AB and CD, find BE and C

 Mar 17, 2022
edited by Guest  Mar 17, 2022
 #1
avatar+117162 
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The first thing you have to do is draw a pic.

You probably won't get it right the first time.

You have to tweak it, and redraw it, a few times until it is right.

Have you done that?

If so, upload a pic of  it, or just describe what you pic looks like.

 

after that you can use cosine rule twice and then solve them the best you can simultaneously

 

I won't say more until you have contributed something of your own.

 Mar 19, 2022
 #2
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Hello! Thank you for the tip!! So far. I have drawn a large triangle with a similar smaller triangle inside. I will attemp to upload the picture, however I am new to the forum and am not sure of the tools used. for reference, AED is the larger triangle will BEC is the  smaller and similar triangle inside. I assumed that it was isoceles, but i am probably wrong 🥲. Because I am at an ameuteur geometry level, I attempted to solve this problem with similar triangles, but that led to the solution of 77/19, which I am decently sure is incorrect. Any help is appreciated. Thanks again!

Guest Mar 19, 2022
 #3
avatar+117162 
+1

Thanks for that great interaction.

I think you have drawn the triangle correctly.

It does not work out to be isosceles.

 

I let the two unknown lengths be x and y

 

then I formed two equations using the cosint rule, one beginning with  26^2=    and the other with  7^2=

then I solved them simultateously (with subtraction) to get an expression for y in terms of x.

then i subed back into an original equation to get two numbers for x, 

[One is actually x and the other is y becasue the terms are interchangeable] 

 

See how much that helps.

 

* Note that my method may not be the best method.

Melody  Mar 19, 2022

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