Regarding n points placed within a circle, and point Q on the periphery.

[frusciante]

Regarding n points placed within/outside of a circle, and point Q on the periphery.

I have been looking at this problem for hours! If anyone could comment on how to proceed I'd be very grateful.

"Given a circle with radius 1 and n=>1 points (P1, P2, ... Pn), Show that a point Q can be placed on the circle periphery such that QP1 + QP2 + ... + QPn => n".
If it helps, here is an illustration;

https://gyazo.com/a57296cc51eee19b986bc647c5f08507

 

[Harry_the_cat]

I have been looking at this problem for hours! If anyone could comment on how to proceed I'd be very grateful.

"Given a circle with radius 1 and n=>1 points (P1, P2, ... Pn), Show that a point Q can be placed on the circle periphery such that Q*P1 + Q*P2 + ... + Q*Pn => n".
If it helps, here is an illustration;

https://gyazo.com/a57296cc51eee19b986bc647c5f08507

Does Q*P1 mean the length between Q and P1 ?

 

[frusciante]

Does Q*P1 mean the length between Q and P1 ?

Indeed, I apologise for that miss. Other than that, the question is stated exactly the way I have written. Also, point Pn is indeed located outside of the circle periphery.

 

[frusciante]

If so, then line QP1 can be .25 (as example),
so lesser than n (since n=1 at this point).

Quite a confusing UNCLEAR problem, hey Harry?

I agree that it is confusing. I was thinking of perhaps proving the ratio of the circumference of the object QP1 QP2 QP3 ... QPn and somehow relating it to ptolemy's theorem with the object in the circle.