Disproving a point on a circle (1 Viewer)

[nrlwinner]

28. A, B, C are three points on a circle and triangle ABC is acute-angled. AD is drawn parallel to BC and CD is drawn parallal to BA. Prove that D cannot lie on the circle. (D is the point of intersection of the two parallels)

I haven't done any work on disproving a point. Do you use cyclic quadralateral?<!-- google_ad_section_end --></SPAN>

 

[jet]

Okay, so, in order for D to lie on the circle, it must form a cyclic quadrilateral with A, B and C, thus,
angle D = 180 - angle B.
But, since ABCD is a parallelogram (AB || CD, AD || BC), angle D = angle B. Thus, ABCD is only a cyclic quadrilateral if angle B = angle D = 90°. BUT, since ABC is an acute-angled triangle, angle B must be less than 90° degrees.
Similar reasoning works for angles A and C.
Hence, ABCD cannot be a cyclic quadrilateral, as opposite angles aren't supplementary, and, therefore, D does not lie on the circle.