9.6
Problems(3)
square inscribed in rhombus (IV Soros Olympiad 1997-98 Correspondence 9.6)
Source:
6/1/2024
A rhombus is circumscribed around a square with side . Find its diagonals if it is known that they are equal to different integers.
geometryrhombus
cut acute triangle into 4 parts (IV Soros Olympiad 1997-98 R3 9.6)
Source:
6/1/2024
Cut an acute triangle, one of whose sides is equal to the altitude drawn, by two straight cuts, into four parts, from which you can fold a square.
geometrycombinatorial geometrycombinatorics
ratio on a chord of a cyclic quad
Source: IV Soros Olympiad 1997-98 R2 9.6 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
6/1/2024
A chord is drawn through the intersection point of the diagonals of an inscribed quadrilateral. It is known that the parts of this chord located outside the quadrilateral have lengths equal to and of this chord. In what ratio is this chord divided by the intersection point of the diagonals of the quadrilateral?
geometrycyclic quadrilateral