MathDB

angle bisector, 80-70-30 triangle (2018 Romania District VII p4)

Source:

May 21, 2020

geometryangle bisectorangles

Problem Statement

Let

ABC

be a triangle with

\angle A = 80^o

and

\angle C = 30^o

. Consider the point

M

inside the triangle

ABC

so that

\angle MAC= 60^o

and

\angle MCA = 20^o

. If

N

is the intersection of the lines

BM

and

AC

to show that a

MN

is the bisector of the angle

\angle AMC