Find the length of CF given a rectangle

N

novodexx

New member
Joined
Jul 7, 2020
Messages
6
Hi All,
I am stuck in the question, I have spent several hours, still no luck:
ABCD is a rectangle, point E is on the AB side, F is on the CE side, and ∠ACD=∠DAF.
If ∠CAF=∠ECB and EB=1, what is the length of CF?
Very appreciated for any help!
rectangle.png
 
Hello, I am a teacher for 9th grade in China (junior hight school), I have tried a lot, and now I can tell ∠EAF=∠EFA=∠DAC，but no idea for further investigation. also drawing a lot full of 4 A4 paper with no luck, and I discussed with my friend who said it could be solved by Trigonometric function， but I think it is a geometry question, should be solved by adding some auxiliary line.
 
Last edited:
I'd like to know a little more. You say that you "think it is a geometry question"; does that mean it is not from the course you teach, but from some other source? It looks to me like a contest-type problem. Is there a specific reason you think trigonometry is inappropriate?

I'll see what I can do with it geometrically.
 
Hi Dr.Peterson, this is not a contest-type one, but a question from 8th grade final exam. Just feel it is a geometry problem. no specific reason, thanks.
 
Hi Dr.Peterson, only 9th grade students in China know trigonometry function.
 
Very nice; you constructed CG with angle y. This is a challenging question for a final exam!
 
You must log in or register to reply here.
Top