MathDB

Let

ABC

be an acute-angled triangle. The lines

L_{A}

L_{B}

and

L_{C}

are constructed through the vertices

A

B

and

C

respectively according the following prescription: Let

H

be the foot of the altitude drawn from the vertex

A

to the side

BC

; let

S_{A}

be the circle with diameter

AH

; let

S_{A}

meet the sides

AB

and

AC

M

and

N

respectively, where

M

and

N

are distinct from

A

; then let

L_{A}

be the line through

A

perpendicular to

MN

. The lines

L_{B}

and

L_{C}

are constructed similarly. Prove that the lines

L_{A}

L_{B}

and

L_{C}

are concurrent.

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