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Prove that FI and BC are perpendicular

Source: Moldova IMO-BMO TST 2003, day 2, problem 3.

August 16, 2008

geometryincenterangle bisector

Problem Statement

The sides

[AB]

and

[AC]

of the triangle

ABC

are tangent to the incircle with center

I

of the

\triangle ABC

at the points

M

and

N

, respectively. The internal bisectors of the

\triangle ABC

drawn form

FI\perp BC

and

C

intersect the line

MN

at the points

P

and

Q

, respectively. Suppose that

F

is the intersection point of the lines

CP

and

BQ

. Prove that

FI\perp BC

.

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