MathDB

1

Part of 2011 China Second Round Olympiad

Problems(2)

two angles are equal

Source: 2011-2012 china second round,problem 1

10/30/2011
Let P,QP,Q be the midpoints of diagonals AC,BDAC,BD in cyclic quadrilateral ABCDABCD. If ∠BPA=∠DPA\angle BPA=\angle DPA, prove that ∠AQB=∠CQB\angle AQB=\angle CQB.
geometrycircumcirclesymmetrycyclic quadrilateralgeometry proposed
Set

Source:

1/30/2012
Let the set A=(a1,a2,a3,a4)A=(a_{1},a_{2},a_{3},a_{4}) . If the sum of elements in every 3-element subset of AA makes up the set B=(−1,5,3,8)B=(-1,5,3,8) , then find the set AA.