MathDB

1

Part of 2002 China National Olympiad

Problems(2)

express BE with a,b,c

Source: 2002 China National Olmpiad

2/14/2012
the edges of triangle ABCABC are a,b,ca,b,c respectively,b<cb<c,ADAD is the bisector of ∠A\angle A,point DD is on segment BCBC. (1)find the property ∠A\angle A,∠B\angle B,∠C\angle C have,so that there exists point E,FE,F on AB,ACAB,AC satisfy BE=CFBE=CF,and ∠NDE=∠CDF\angle NDE=\angle CDF (2)when such E,FE,F exist,express BEBE with a,b,ca,b,c
geometrygeometric transformationangle bisectorgeometry proposed
4 vertices on the plane

Source: 2002 China National Olmpiad

2/14/2012
For every four points P1,P2,P3,P4P_{1},P_{2},P_{3},P_{4} on the plane, find the minimum value of ∑1≤ i<j≤ 4PiPjmin⁡1≤ i<j≤ 4(PiPj)\frac{\sum_{1\le\ i<j\le\ 4}P_{i}P_{j}}{\min_{1\le\ i<j\le\ 4}(P_{i}P_{j})}.
geometry proposedgeometry