MathDB

Let

ABC

be a right-angled triangle with

\angle BAC = 90^{\circ}

. Let the height from

A

cut its side

BC

D

. Let

I, I_B, I_C

be the incenters of triangles

ABC, ABD, ACD

respectively. Let also

EB, EC

be the excenters of

ABC

with respect to vertices

B

and

C

respectively. If

K

is the point of intersection of the circumcircles of

E_CIB_I

and

E_BIC_I

, show that

KI

passes through the midpoint

M

of side

BC

G4