MathDB

2

Part of 1995 Cono Sur Olympiad

Problems(2)

Segments

Source: Cono Sur Olympiad, 1995, Prbblem #2

5/28/2006
There are ten points marked on a circumference, numbered from 11 to 1010 and join all points with segments. I color the segments, with red someones and others with blue. Without changing the colors of the segments, renumber all the points from the 11 to the 1010. Will be possible to color the segments and to renumber the points so that those numbers that were jointed with red are jointed now with blue and the numbers that were jointed with blue they are jointed now with red?
Find the area

Source: Cono Sur Olympiad, 1995, Problem #5

5/28/2006
The semicircle with centre OO and the diameter ACAC is divided in two arcs ABAB and BCBC with ratio 1:31: 3. MM is the midpoint of the radium OCOC. Let TT be the point of arc BCBC such that the area of the cuadrylateral OBTMOBTM is maximum. Find such area in fuction of the radium.
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