Triangle problem

K

kasd

New member
Joined
Dec 28, 2020
Messages
15
Hello,
I'm trying to solve this problem but I have no idea how to continue my solution in order to reach the end. I know what I need to prove but I don't know how. please help

Point F belongs to side BC in the triangle ABC such that AC=BF. Prove that the line starting from the median of CF and parallel to L <)ACB intersects with the median of AB.
My solution (NOT FULL):
Let M be the median of CF, M1 be the median of AB and CL be the bisector of <)ACB. Let E be the median of AF. Therefore triangle M1ME is an isosceles triangle (EM and EM1 are middle segments of AC and BF and AC=BF). I somehow need to prove that <)MEM1=0,5*<)ACB so that CL and MM1 will be parallel.
Please show me how to do so. Thanks in advance : -)
 
kasd said:
Hello,
I'm trying to solve this problem but I have no idea how to continue my solution in order to reach the end. I know what I need to prove but I don't know how. please help

Point F belongs to side BC in the triangle ABC such that AC=BF. Prove that the line starting from the median of CF and parallel to L <)ACB intersects with the median of AB.
My solution (NOT FULL):
Let M be the median of CF, M1 be the median of AB and CL be the bisector of <)ACB. Let E be the median of AF. Therefore triangle M1ME is an isosceles triangle (EM and EM1 are middle segments of AC and BF and AC=BF). I somehow need to prove that <)MEM1=0,5*<)ACB so that CL and MM1 will be parallel.
Please show me how to do so. Thanks in advance : -)
Click to expand...
Could you post a diagram?
 
kasd said:
Point F belongs to side BC in the triangle ABC such that AC=BF. Prove that the line starting from the median of CF and parallel to L <)ACB intersects with the median of AB.
Click to expand...
Please define what you mean by the median of a segment, and by "L <)ACB".
 
kasd said:
please help, the competition is tomorrow, it's urgent!
Click to expand...
What competition? Why do you need an answer before then?

In any case, please comply with the request for a diagram of what you have done so far, to help us follow it.

Okay, here is my picture of what you describe:
1613149196866.png

You've done some good thinking so far. (My N is the intersection with the line, which we want to show is identical to M1.) Unfortunately, I have to go do other things.
 
Last edited:
This is a problem from the last year edition of the compeititon. The diagram is exactly right
 
I solved it. Thank you by the way. Have a great weekend : )
 
You must log in or register to reply here.
Top