MathDB

K on (ABI) if and only if K is on (CDJ)

Source: Benelux 2009

January 29, 2011

geometrytrapezoidcircumcirclegeometry proposed

Problem Statement

Given trapezoid

ABCD

with parallel sides

AB

and

CD

, let

E

be a point on line

BC

outside segment

BC

, such that segment

AE

intersects segment

CD

. Assume that there exists a point

F

inside segment

AD

such that

\angle EAD=\angle CBF

. Denote by

I

the point of intersection of

CD

and

EF

, and by

J

the point of intersection of

AB

and

EF

. Let

K

be the midpoint of segment

EF

, and assume that

K

is different from

I

and

J

.
Prove that

K

belongs to the circumcircle of

\triangle ABI

if and only if

K

belongs to the circumcircle of

\triangle CDJ

.

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