MathDB

1

Part of 1995 Turkey Team Selection Test

Problems(2)

Find all solutions to the system

Source: Turkey IMO TST 1995 #1

7/8/2011
Given real numbers b≥a>0b \geq a>0, find all solutions of the system \begin{align*} &x_1^2+2ax_1+b^2=x_2,\\ &x_2^2+2ax_2+b^2=x_3,\\ &\qquad\cdots\cdots\cdots\\ &x_n^2+2ax_n+b^2=x_1. \end{align*}
algebrapolynomialalgebra unsolved
Find angle measure in convex quadrilateral

Source: Turkey IMO TST 1995 #4

7/8/2011
In a convex quadrilateral ABCDABCD it is given that ∠CAB=40∘,∠CAD=30∘,∠DBA=75∘\angle{CAB} = 40^{\circ}, \angle{CAD} = 30^{\circ}, \angle{DBA} = 75^{\circ}, and ∠DBC=25∘\angle{DBC}=25^{\circ}. Find ∠BDC\angle{BDC}.
geometryperpendicular bisectorangle bisectorgeometry unsolved