MathDB

2

Part of 2006 Turkey Team Selection Test

Problems(2)

Ways to divide a rectangle in integer rectangles

Source: Turkey, TST D1, P2

5/10/2006
How many ways are there to divide a 2×n2\times n rectangle into rectangles having integral sides, where nn is a positive integer?
geometryrectanglecalculusintegrationfunctioncombinatorics proposedcombinatorics
Prove that CD bisects QH

Source: Turkey, TST D2, P2

5/10/2006
From a point QQ on a circle with diameter ABAB different from AA and BB, we draw a perpendicular to ABAB, QHQH, where HH lies on ABAB. The intersection points of the circle of diameter ABAB and the circle of center QQ and radius QHQH are CC and DD. Prove that CDCD bisects QHQH.
Eulergeometryangle bisectorpower of a pointradical axisgeometry proposed