MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2019 Latvia Baltic Way TST
11
11
Part of
2019 Latvia Baltic Way TST
Problems
(1)
Metric relation in regular 2018- gon
Source: Latvian TST for Baltic Way 2019, Problem 11
6/4/2020
Let
A
1
A
2
.
.
.
A
2018
A_1A_2...A_{2018}
A
1
A
2
...
A
2018
be regular
2018
2018
2018
-gon. Radius of it's circumcircle is
R
R
R
. Prove that:
A
1
A
1008
−
A
1
A
1006
+
A
1
A
1004
−
A
1
A
1002
+
.
.
.
+
A
1
A
4
−
A
1
A
2
=
R
A_1A_{1008}-A_1A_{1006}+A_1A_{1004}-A_1A_{1002} + ... + A_1A_4 -A_1A_2=R
A
1
A
1008
−
A
1
A
1006
+
A
1
A
1004
−
A
1
A
1002
+
...
+
A
1
A
4
−
A
1
A
2
=
R
geometry
circumcircle