MathDB

Ratio - Switzerland 2011

Source:

March 22, 2011

ratiogeometrycircumcircleperpendicular bisectorgeometry proposed

Problem Statement

Let

\triangle{ABC}

be a triangle with circumcircle

\tau

. The tangentlines to

\tau

through

A

and

B

intersect at

T

. The circle through

A

,

B

and

T

intersects

BC

and

AC

again at

D

and

E

, respectively;

CT

and

BE

intersect at

F

. Suppose

D

is the midpoint of

BC

. Calculate the ratio

BF:BE

.
(Swiss Mathematical Olympiad 2011, Final round, problem 5)

Back to Problems View on AoPS