MathDB

Collinearity of orthocentres

Source: China TST 2006

June 18, 2006

geometrycircumcircleparallelogram3D geometrytetrahedrongeometric transformationhomothety

Problem Statement

Let

K

and

M

be points on the side

AB

of a triangle

\triangle{ABC}

, and let

L

and

N

be points on the side

AC

. The point

K

is between

M

and

B

, and the point

L

is between

N

and

C

. If

\frac{BK}{KM}=\frac{CL}{LN}

, then prove that the orthocentres of the triangles

\triangle{ABC}

,

\triangle{AKL}

and

\triangle{AMN}

lie on one line.

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