MathDB

KM.LN=BM.CN

Source: Turkey TST 2013 - Day 2 - P2

April 2, 2013

geometryincenterratiotrigonometrygeometry proposed

Problem Statement

Let the incircle of the triangle

ABC

touch

[BC]

at

D

and

I

be the incenter of the triangle. Let

T

be midpoint of

[ID]

. Let the perpendicular from

I

to

AD

meet

AB

and

AC

at

K

and

L

, respectively. Let the perpendicular from

T

to

AD

meet

AB

and

AC

at

M

and

N

, respectively. Show that

|KM|\cdot |LN|=|BM|\cdot|CN|

.

Back to Problems View on AoPS