MathDB

isosceles trapezoid in a greek jmbo tst from 2013

Source: Greece JBMO TST 2013 p4

April 29, 2019

geometrytrapezoidisosceles

Problem Statement

Given the circle

c(O,R)

(with center

O

and radius

K

), one diameter

OA

and midpoint

CD,CO

of the arc

AB

. Consider circle

c_1(K,KO)

, where center

K

lies on the segment

OA

, and consider the tangents

CD,CO

from the point

E

to circle

Z

. Line

KD

intersects circle

c(O,R)

at points

E

and

Z

(point

E

lies on the semicircle that lies also point

C

). Lines

EC

and

CZ

intersects

AB

at points

N

and

M

respectively. Prove that quadrilateral

EMZN

is an isosceles trapezoid, inscribed in a circle whose center lie on circle

c(O,R)

.

Back to Problems View on AoPS