MathDB

In the acute isosceles triangle

ABC

the altitudes

BB_1

and

CC_1

are drawn, which intersect at the point

H

. Let

L_1

and

L_2

be the feet of the angle bisectors of the triangles

B_1AC_1

and

B_1HC_1

drawn from vertices

A

and

H

, respectively. The circumscribed circles of triangles

AHL_1

and

AHL_2

intersects the line

B_1C_1

for the second time at points

P

and

Q

, respectively. Prove that points

B, C, P

and

Q

lie on the same circle.
(M. Plotnikov, D. Hilko)

Problem Statement