MathDB

2

Part of 2010 Lithuania National Olympiad

Problems(2)

bisector of A

Source: Lithuania NMO 2010,problem 2

3/11/2012
In trapezoid ABCDABCD, ADAD is parallel to BCBC. Knowing that AB=AD+BCAB=AD+BC, prove that the bisector of ∠A\angle A also bisects CDCD.
geometrytrapezoidangle bisectorgeometry unsolved
find angle B

Source: Lithuania NMO 2010

3/11/2012
Let II be the incenter of a triangle ABCABC. D,E,FD,E,F are the symmetric points of II with respect to BC,AC,ABBC,AC,AB respectively. Knowing that D,E,F,BD,E,F,B are concyclic,find all possible values of ∠B\angle B.
geometryincentercircumcircleinradiusperpendicular bisectorgeometry unsolved