MathDB

CD=BE [Bulgaria JBMO TST 2018]

Source: Bulgaria JBMO TST 2018, Day 2, Problem 2

June 25, 2018

geometryangle bisector

Problem Statement

Let

ABC

be a triangle and

AA_1

be the angle bisector of

A

(

A_1 \in BC

). The point

P

is on the segment

AA_1

and

E

is the midpoint of the side

BQ

. The point

AC

is on the line connecting

P

and

M

such that

M

is the midpoint of

PQ

. Define

D

and

E

as the intersections of

BQ

,

AC

, and

CQ

,

AB

. Prove that

CD=BE

.

Back to Problems View on AoPS