MathDB

BE=EZ=ZC, ratio of areas, equilateral (Greece Juniors 1997 p1)

Source:

March 16, 2020

geometryangle bisectorperpendicular bisectorratio

Problem Statement

Let

ABC

be an equilateral triangle whose angle bisectors of

B

and

C

intersect at

D

. Perpendicular bisectors of

BD

and

CD

intersect

BC

at points

E

and

Z

respectively. a) Prove that

BE=EZ=ZC

. b) Find the ratio of the areas of the triangles

BDE

ABC