MathDB

angles wanted, <ABD = <CBD, 3<ACE = 2<BCE, CD = DE = CH

Source: 2008 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p7

April 28, 2021

geometryequal anglesequal segmentsUkraine Correspondence

Problem Statement

On the sides

AC

and

AB

of the triangle

ABC

, the points

D

and

E

were chosen such that

\angle ABD =\angle CBD

and

3 \angle ACE = 2\angle BCE

. Let

H

be the point of intersection of

BD

and

CE

, and

CD = DE = CH

. Find the angles of triangle

ABC