MathDB

4

Part of 2012 Czech-Polish-Slovak Junior Match

Problems(2)

3 of 51 vertices of 101-regular polygon are vertices of an isosceles

Source: Czech-Polish-Slovak Junior Match 2012, Individual p4 CPSJ

3/11/2020
Prove that among any 5151 vertices of the 101101-regular polygon there are three that are the vertices of an isosceles triangle.
polygonregular polygoncombinatoricscombinatorial geometryisosceles
computational inside a rhombus with an angle 60^o

Source: Czech-Polish-Slovak Junior Match 2012, Team p4 CPSJ

3/12/2020
A rhombus ABCDABCD is given with ∠BAD=60o\angle BAD = 60^o . Point PP lies inside the rhombus such that BP=1BP = 1, DP=2DP = 2, CP=3CP = 3. Determine the length of the segment APAP.
geometryrhombusSegment