MathDB

4

Part of 2004 Indonesia MO

Problems(2)

Intersecting circles

Source: Indonesia Mathematics Olympiad 2004 Day 1 Problem 4

10/22/2009
There exists 4 circles, a,b,c,d a,b,c,d, such that a a is tangent to both b b and d d, b b is tangent to both a a and c c, c c is both tangent to b b and d d, and d d is both tangent to a a and c c. Show that all these tangent points are located on a circle.
PIE sure looks good...

Source: Indonesia Mathematics Olympiad 2004 Day 2 Problem 4

10/22/2009
8. Sebuah lantai luasnya 3 meter persegi ditutupi lima buah karpet dengan ukuran masing-masing 1 meter persegi. Buktikan bahwa ada dua karpet yang tumpang tindih dengan luas tumpang tindih minimal 0,2 meter persegi. A floor of a certain room has a 3 m2 3 \ m^2 area. Then the floor is covered by 5 rugs, each has an area of 1 m2 1 \ m^2. Prove that there exists 2 overlapping rugs, with at least 0.2 m2 0.2 \ m^2 covered by both rugs.
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