MathDB

Let

A

be point in the exterior of the circle

\mathcal C

. Two lines passing through

A

intersect the circle

\mathcal C

in points

B

and

C

(with

B

between

A

and

C

) respectively in

D

and

E

(with

D

between

A

and

E

). The parallel from

D

BC

intersects the second time the circle

\mathcal C

F

. Let

G

be the second point of intersection between the circle

\mathcal C

and the line

AF

and

M

the point in which the lines

AB

and

EG

intersect. Prove that

\frac 1{AM} = \frac 1{AB} + \frac 1{AC}.

Problem Statement