1)

AB, AC are two equal chords of a circle. AP is another chord of the circle which cuts BC at Q. Prove AP.AQ = AB

2)

ABC is an isosceles triangle in which AB = AC and BC>AB. X is a point on CA produced. Y is a point on BC such that angle(BYX)=2angle(YXC). Show that AXBY is a cyclic quadrilateral.

Thx