MathDB

3

Part of 2008 Federal Competition For Advanced Students, Part 2

Problems(2)

Construct a square with a straightedge and compass

Source: Austrian Mathematical Olympiad 2008 Problem 3

2/6/2009
We are given a line g g with four successive points P P, Q Q, R R, S S, reading from left to right. Describe a straightedge and compass construction yielding a square ABCD ABCD such that P P lies on the line AD AD, Q Q on the line BC BC, R R on the line AB AB and S S on the line CD CD.
geometrygeometric transformationreflectiongeometry unsolved
Determine the set of all acceptable points

Source: Austrian Mathematical Olympiad 2008 Problem 6

2/6/2009
We are given a square ABCD ABCD. Let P P be a point not equal to a corner of the square or to its center M M. For any such P P, we let E E denote the common point of the lines PD PD and AC AC, if such a point exists. Furthermore, we let F F denote the common point of the lines PC PC and BD BD, if such a point exists. All such points P P, for which E E and F F exist are called acceptable points. Determine the set of all acceptable points, for which the line EF EF is parallel to AD AD.
geometrycircumcirclegeometric transformationreflectiongeometry unsolved