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Regional Olympiad - FBH 2010 Grade 9 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2010

September 27, 2018

geometryCyclicquadrilateral

Problem Statement

In convex quadrilateral

ABCD

, diagonals

AC

and

BD

intersect at point

O

at angle

90^{\circ}

. Let

K

L

M

and

N

be orthogonal projections of point

O

to sides

AB

BC

CD

and

DA

of quadrilateral

ABCD

. Prove that

KLMN

is cyclic