MathDB

In a triangle

\triangle{ABC}

with all its sides of different length,

D

is on the side

AC

, such that

BD

is the angle bisector of

\sphericalangle{ABC}

. Let

E

and

F

, respectively, be the feet of the perpendicular drawn from

A

and

C

to the line

BD

and let

M

be the point on

BC

such that

DM

is perpendicular to

BC

. Show that

\sphericalangle{EMD}=\sphericalangle{DMF}

Problem Statement