MathDB

IMO Shortlist 2009 - Problem G4

Source:

July 5, 2010

geometryIMO Shortlistgeometry solvedcyclic quadrilateralprojective geometrytangentpower of a point

Problem Statement

Given a cyclic quadrilateral

ABCD

, let the diagonals

AC

and

BD

meet at

E

and the lines

AD

and

BC

meet at

F

. The midpoints of

AB

and

CD

are

G

and

H

, respectively. Show that

EF

is tangent at

E

to the circle through the points

E

,

G

and

H

.
Proposed by David Monk, United Kingdom

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