MathDB

2

Part of 1998 IberoAmerican

Problems(2)

13rd ibmo - rep. dominicana 1998/q2.

Source: Spanish Communities

4/16/2006
The circumference inscribed on the triangle ABCABC is tangent to the sides BCBC, CACA and ABAB on the points DD, EE and FF, respectively. ADAD intersect the circumference on the point QQ. Show that the line EQEQ meet the segment AFAF at its midpoint if and only if AC=BCAC=BC.
geometry unsolvedgeometry
13rd ibmo - rep. dominicana 1998/q5.

Source: Spanish Communities

4/16/2006
Find the maximal possible value of nn such that there exist points P1,P2,P3,…,PnP_1,P_2,P_3,\ldots,P_n in the plane and real numbers r1,r2,…,rnr_1,r_2,\ldots,r_n such that the distance between any two different points PiP_i and PjP_j is ri+rjr_i+r_j.
combinatorics unsolvedcombinatorics