MathDB

3

Part of 2013 Saint Petersburg Mathematical Olympiad

Problems(3)

St.Peterburg, P3 Grade 11, 2013

Source:

4/17/2014
Let MM and NN are midpoint of edges ABAB and CDCD of the tetrahedron ABCDABCD, AN=DMAN=DM and CM=BNCM=BN. Prove that AC=BDAC=BD.
S. Berlov
geometry3D geometrytetrahedronparallelogramgeometry proposed
St.Peterburg, P3 Grade 10, 2013

Source:

4/27/2014
On a circle there are some black and white points (there are at least 1212 points). Each point has 1010 neighbors (55 left and 55 right neighboring points), 55 being black and 55 white. Prove that the number of points on the circle is divisible by 44.
combinatorics proposedcombinatorics
Bisectors and parallels

Source: St Petersburg Olympiad 2013, Grade 9, P3

10/13/2017
ABCABC is triangle. l1l_1- line passes through AA and parallel to BCBC, l2l_2 - line passes through CC and parallel to ABAB. Bisector of ∠B\angle B intersect l1l_1 and l2l_2 at X,YX,Y. XY=ACXY=AC. What value can take ∠A−∠C\angle A- \angle C ?
geometry