geometry(iranian geometry olympiad 2017)

Latest News, Announcements, and Forum Rules
abrarfiaz
Posts: 14
Joined: Mon Mar 20, 2017 4:53 pm

geometry(iranian geometry olympiad 2017)

4. P1,P2,...,P100 are 100 points on the plane, no three of them are collinear. For each three points, call their triangle clockwise if the increasing order of them is in clockwise order. Can the number of clockwise triangles be exactly 2017?

help me solving the problem
"God made the integers; all else is the work of man."

Posts: 181
Joined: Mon Mar 28, 2016 6:21 pm

Re: geometry(iranian geometry olympiad 2017)

What help do you need?
Frankly, my dear, I don't give a damn.

abrarfiaz
Posts: 14
Joined: Mon Mar 20, 2017 4:53 pm

Re: geometry(iranian geometry olympiad 2017)

I am being unable of understanding the main concept of the problem. Truly to say ,can't understand the problem. I would be grateful if you do help me
"God made the integers; all else is the work of man."

Posts: 181
Joined: Mon Mar 28, 2016 6:21 pm

Re: geometry(iranian geometry olympiad 2017)

Okay so you're having difficulty in understanding what clockwise is. In the picture \$ABC\$ is clockwise and \$A_1B_1C_1\$ is counterclockwise.
Attachments
Screenshot from 2018-02-06 13-12-01.png (26.11 KiB) Viewed 689 times
Frankly, my dear, I don't give a damn.

samiul_samin
Posts: 999
Joined: Sat Dec 09, 2017 1:32 pm

Re: geometry(iranian geometry olympiad 2017)

abrarfiaz wrote:
Mon Feb 05, 2018 7:54 pm
I am being unable of understanding the main concept of the problem. Truly to say ,can't understand the problem. I would be grateful if you do help me
Sketch of the solution