MathDB
rectangle / square inscribed in rhombus

Source: Polish MO second round 1952 p3

August 28, 2024
geometryrectangleinscribedsquarerhombus

Problem Statement

Are the following statements true?
a) if the four vertices of a rectangle lie on the four sides of a rhombus, then the sides of the rectangle are parallel to the diagonals of the rhombus;
b) if the four vertices of a square lie on the four sides of a rhombus that is not a square, then the sides of the square are parallel to the diagonals of the rhombus.