MathDB

An acute triangle is a triangle that has all angles less that

90^{\circ}

(

90^{\circ}

is a Right Angle). Let

ABC

be a right-angled triangle with

\angle ACB =90^{\circ}.

Let

CD

be the altitude from

C

AB,

and let

E

be the intersection of the angle bisector of

\angle ACD

with

AD.

Let

EF

be the altitude from

E

BC.

Prove that the circumcircle of

BEF

passes through the midpoint of

CE.

Problem Statement