MathDB

Suppose that

ABCD

is a cyclic quadrilateral. Let E \equal{} AC\cap BD and F \equal{} AB\cap CD. Denote by

H_{1}

and

H_{2}

the orthocenters of triangles

EAD

and

EBC

, respectively. Prove that the points

F

H_{1}

H_{2}

are collinear.
Original formulation:
Let

ABC

be a triangle. A circle passing through

B

and

C

intersects the sides

AB

and

AC

again at

C'

and

B',

respectively. Prove that

BB'

CC'

and

HH'

are concurrent, where

H

and

H'

are the orthocentres of triangles

ABC

and

AB'C'

respectively.

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