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Sprint Camp AIME

 
 
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Sprint Camp AIME
by Ethan Sun - Tuesday, January 16, 2024, 8:00 PM
 

Hello! For the week 6 homework, I am sort of stuck on question 6...

I would like an idea for it, currently I have tried abusing the isosceles triangle ABC and have tried reflecting D across the height of ABC...

Currently I do not know how to proceed, thank you!

 
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Re: Sprint Camp AIME
by Ethan Sun - Wednesday, January 17, 2024, 10:51 AM
 

Oop, I was able to solve the problem now!

I set AB = AC = x, and AE as y, EC = z.

Then I solved the system of equations

After finding the lengths, I used ptolemy's, and since we know the ratio of the similar triangles we can find BC.

Finally, we can finish the problem with an "inverse" of LoC.

 
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Re: Sprint Camp AIME
by Dr. Kevin Wang - Friday, January 19, 2024, 10:55 PM
 

Very good! You can also review the question and the solution will be shown (may be different from yours---it is nice to have multiple solutions for the same problem).

 
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