MathDB

AB= CE wanted, starting with a 90-54-36 triangle

Source: 2015 Moldova JBMO TST 2.3

July 11, 2020

geometryright triangleequal segments

Problem Statement

In a right triangle

ABC

with

\angle BAC =90^o

and

\angle ABC= 54^o

, point

M

is the midpoint of the hypotenuse

[BC]

, point

D

is the foot of the angle bisector drawn from the vertex

C

and

AM \cap CD = \{E\}

. Prove that

AB= CE