In the same plane,two circles can have a maximum of ............ common chords.

In an isosceles triangle $ABC$ with $AB = AC$,a circle passing through $B$ and $C$ intersects the sides $AB$ and $AC$ at $X$ and $Y$ respectively. Prove that $XY \parallel BC$.

If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides,prove that the quadrilateral so formed is cyclic.

In a circle with centre $P$,$AB$ and $CD$ are equal chords. If $\angle APB = 80^{\circ}$,then find $\angle CPD$. (in $^{\circ}$)

Prove that among all the chords of a circle passing through a given point inside the circle,the one that is perpendicular to the diameter passing through the point is the smallest.

In a circle with centre $P$,$AB$ and $CD$ are chords. If $\angle APB = 80^{\circ}$,$\angle CPD = 50^{\circ}$ and $AB = 7\, cm$,then find the length of chord $CD$. (in $, cm$)