MathDB

3

Part of 2013 Bundeswettbewerb Mathematik

Problems(2)

BWM 2013 P3: P is a point in ABCD. Find angle PBA

Source:

6/4/2014
In the interior of the square ABCDABCD, the point PP lies in such a way that ∠DCP=∠CAP=25∘\angle DCP = \angle CAP=25^{\circ}. Find all possible values of ∠PBA\angle PBA.
BWM 2013 P7: Hexagon whose vertices lie on a circle

Source:

6/6/2014
Let ABCDEFABCDEF be a convex hexagon whose vertices lie on a circle. Suppose that AB⋅CD⋅EF=BC⋅DE⋅FAAB\cdot CD\cdot EF = BC\cdot DE\cdot FA. Show that the diagonals AD,BEAD, BE and CFCF are concurrent.