MathDB

2011.89.4

Part of Kyiv City MO Juniors 2003+ geometry

Problems(1)

<DKL=<CLK if <BMN=<MNC, midpoints of cyclic (2011 Kyiv City MO 9.4)

Source:

7/14/2020
Let ABCDABCD be an inscribed quadrilateral. Denote the midpoints of the sides AB,BC,CDAB, BC, CD and DADA through M,L,NM, L, N and KK, respectively. It turned out that ∠BMN=∠MNC\angle BM N = \angle MNC. Prove that: i) ∠DKL=∠CLK\angle DKL = \angle CLK. ii) in the quadrilateral ABCDABCD there is a pair of parallel sides.
geometryCyclicequal anglesmidpoints