MathDB

1

Part of 2005 Slovenia Team Selection Test

Problems(1)

if MA\cdot MC + MA\cdot CD = MB \cdot MD then <BKC =< BDC

Source: Slovenia TST 2005 p1

2/15/2020
The diagonals of a convex quadrilateral ABCDABCD intersect at MM. The bisector of ∠ACD\angle ACD intersects the ray BABA at KK. Prove that if MA⋅MC+MA⋅CD=MB⋅MDMA\cdot MC + MA\cdot CD = MB \cdot MD , then ∠BKC=∠BDC\angle BKC = \angle BDC
equal anglesgeometrydiagonals