Online Course Discussion Forum

P10 from week 2 day 2

 
 
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P10 from week 2 day 2
by Henry Zhang - Monday, 27 July 2020, 11:15 AM
 

P10: Given  triangle ABC,  erect  externally  equilateral  triangle P3 on  side AB and  regular hexagon P6 on  side AC. Let D and E be  the  centers  of P3 and P6,  respectively.   Let F be the midpoint of side BC.  Compute ∠DFE.

I got the correct answer by choosing an easy example where ABC is a right triangle, but there is probably a more rigorous way to show that it's 90 degrees for any triangle ABC. Could I maybe get some hints toward how to do that?



 
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Re: P10 from week 2 day 2
by Dr. Kevin Wang - Monday, 10 August 2020, 12:14 AM
 

Try a rotation of the entire diagram about the point $F$ by 180 degrees.