MathDB

2

Part of 2004 Tuymaada Olympiad

Problems(2)

Tuymaada pb

Source: Tuymaada 2004

6/29/2005
In the plane are given 100 lines such that no 2 are parallel and no 3 meet in a point. The intersection points are marked. Then all the lines and k of the marked points are erased. Given the remained points of intersection for what max k one can reconstruct the lines?
Proposed by A. Golovanov
combinatorics proposedcombinatorics
Incircle, circumcircle.. one angle to compute.

Source: Tuymaada 2004, day 2, problem 2. - Author : A. Smirnov.

5/25/2007
The incircle of triangle ABCABC touches its sides ABAB and BCBC at points PP and Q.Q. The line PQPQ meets the circumcircle of triangle ABCABC at points XX and Y.Y. Find ∠XBY\angle XBY if ∠ABC=90∘.\angle ABC = 90^\circ.
Proposed by A. Smirnov
geometrycircumcirclegeometry proposed