MathDB

Consider a convex quadrilateral

ABCD

. Pairs of its opposite sides are continued until they intersect:

BA

and

CD

at the point

P

BC

and

AD

at the point

Q

. Let

K

be the intersection point of the exterior bisectors of the angles

A

and

C

of the quadrilateral,

L

be the intersection point of the exterior bisectors of the angles

B

and

D

of the quadrilateral, and

M

be the intersection point of the exterior bisectors of the angles

P

and

Q

(the exterior bisector of an angle

X

is the line passing through X and perpendicular to its ordinary bisector). Prove that the points

K

L

and

M

lie on a straight line.
(S Markelov)

Problem Statement