MathDB

ABC

is an isosceles triangle with

AB=AC

and the angle in

A

is less than

60^{\circ}

. Let

D

be a point on

AC

such that

\angle{DBC}=\angle{BAC}

E

is the intersection between the perpendicular bisector of

BD

and the line parallel to

BC

passing through

A

F

is a point on the line

AC

such that

FA=2AC

(

A

is between

F

and

C

). Show that

EB

and

AC

are parallel and that the perpendicular from

F

AB

, the perpendicular from

E

AC

and

BD

are concurrent.

Problem Statement