Let-K-L-M-and-N-be-the-midpoints-of-the-sides-AB-BC-CD-and-DA-respectively-of-a-cyclic-quadrilateral-ABCD-Prove-that-the-orthocenters-of-the-triangles-AKN-BKL-CLM-and-DMN-are-the-vertices-of-

Question Number 16074 by Tinkutara last updated on 17/Jun/17

Let K, L, M and N be the midpoints of

the sides A B, B C, C D and D A,

respectively, of a cyclic quadrilateral

A B C D . Prove that the orthocenters

of the triangles A K N, B K L, C L M and

D M N are the vertices of a

parallelogram .