MathDB

<AOE =? trapezoid ABCD, EF//AB , EF = AD, <AOB=<DAB=90^o

Source: 2005 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-11 p7

April 28, 2021

geometrytrapezoidanglesright angleUkraine Correspondence

Problem Statement

Let

O

be the point of intersection of the diagonals of the trapezoid

ABCD

with the bases

AB

and

CD

. It is known that

\angle AOB = \angle DAB = 90^o

. On the sides

AD

and

BC

take the points

E

and

F

so that

EF\parallel AB

and

EF = AD

. Find the angle

\angle AOE