+0  
 
0
105
4
avatar+146 

Suppose we are given seven points that are equally spaced around a circle. If P, Q, and R are chosen to be any three of these points, then how many different possible values are there for angle PQR?

Mathgenius  Sep 22, 2018
 #1
avatar+3238 
+1

There are a total of \(\dbinom{6}{2}=15\) possible angles

But it turns out that many of the angles are congruent.

 

The 15 angles are made up of 1 + 2 + 3 + 4 + 5 copies of 5 different angles.

 

There are only 5 different possible angles

Rom  Sep 23, 2018
 #2
avatar+94201 
+1

I've played with this a little and Rom's answer is most likely correct but I do not see why.

If I spent hours on proofs I am sure I could show it but I don't see it intuitively at all.

 

I was surprised when that angle came up as 77 degrees.

 

Melody  Sep 23, 2018
 #3
avatar
0

Suppose we have n points equally spaced around a circle. Then there are exactly

 

(n-2) different possible values for the angle PQR and they are 

 

i*(180/n) for 1<=i<=n-2

Guest Sep 24, 2018
 #4
avatar+94201 
0

Ok thanks. 

Do you know why ?

If so would you care to share your knowledge?

Melody  Sep 24, 2018
edited by Melody  Sep 24, 2018

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