MathDB

The altitudes

BB_1

and

CC_1

, are drawn in an acute triangle

ABC

. Let

X

and

Y

be the points, which are symmetrical to the points

B_1

and

C_1

, with respect to the midpoints of the sides

AB

and

AC

of the triangle

ABC

respectively. Let's denote with

Z

the point of intersection of the lines

BC

and

XY

. Prove that the line

ZA

is tangent to the circumscribed circle of the triangle

AXY

Problem Statement