MathDB

5

Part of 2015 Iran Geometry Olympiad

Problems(3)

6 circles in plane such every circle passes through centers of 3 others

Source: IGO 2015 Elementary 5

7/22/2018
Do there exist 66 circles in the plane such that every circle passes through centers of exactly 33 other circles?
by Morteza Saghafian
geometrycirclesCenter
Geometry, circles

Source:

8/28/2017
a) Do there exist 5 circles in the plane such that every circle passes through centers of exactly 3 circles? b) Do there exist 6 circles in the plane such that every circle passes through centers of exactly 3 circles?
geometry
IGO - Hard level - Problem 5

Source:

9/3/2015
we have a triangle ABC ABC and make rectangles ABA1B2 ABA_1B_2 , BCB1C2 BCB_1C_2 and CAC1A2 CAC_1A_2 out of it.
then pass a line through A2 A_2 perpendicular to C1A2 C_1A_2 and pass another line through A1 A_1 perpendicular to A1B2 A_1B_2 .
let A′ A' the common point of this two lines. like this we make B′ B' and C′ C' .
prove AA′ AA' , BB′ BB' and CC′ CC' intersect each other in a same point.
geometryIGO