MathDB

Show that the sum of the angles is equal to 180

Source: Turkey JBMO TST 2014 P1

May 30, 2014

ratiogeometryangle bisectorgeometry proposed

Problem Statement

In a triangle

ABC

, the external bisector of

\angle BAC

intersects the ray

BC

D

. The feet of the perpendiculars from

B

and

C

to line

AD

are

E

and

F

, respectively and the foot of the perpendicular from

D

AC

G

. Show that

\angle DGE + \angle DGF = 180^{\circ}