MathDB

In an acute-angled triangle

ABC

AB > BC

, and the points

A_1

and

C_1

are the feet of the altitudes of from the vertices

A

and

C

. Let

D

be the second intersection of the circumcircles of triangles

ABC

and

A_1BC_1

(different of

B

). Let

Z

be the intersection of the tangents to the circumcircle of the triangle ABC at the points

A

and

C

, and let the lines

ZA

and

A_1C_1

intersect at the point

X

, and the lines

ZC

and

A_1C_1

intersect at the point

Y

. Prove that the point

D

lies on the circumcircle of the triangle

XYZ

2015.7