MathDB

angle bisectors in triangle, segments equal

Source: Bulgaria 1992 P5

May 18, 2021

geometryTriangles

Problem Statement

Points

D,E,F

are midpoints of the sides

AB,BC,CA

of triangle

ABC

. Angle bisectors of the angles

BDC

and

ADC

intersect the lines

BC

and

AC

respectively at the points

M

and

N

, and the line

MN

intersects the line

CD

at the point

O

. Let the lines

EO

and

FO

intersect respectively the lines

AC

and

BC

at the points

P

and

Q

. Prove that

CD=PQ

. (Plamen Koshlukov)

Back to Problems View on AoPS