IZhO 2005 Problem 5

The inner point $X$ of a quadrilateral is observable from the side $YZ$ if the perpendicular to the line $YZ$ meet it in the colosed interval $[YZ].$ The inner point of a quadrilateral is a $k-$ point if it is observable from the exactly $k$ sides of the quadrilateral. Prove that if a convex quadrilateral has a 1-point then it has a $k-$ point for each $k=2,3,4.$