The region between an arc and the two radii,joining the centre to the end points of the arc is called a ........... .

$ABCD$ is a cyclic quadrilateral in which $\angle BAC = 45^{\circ}$ and $\angle ADB = 55^{\circ},$ then $\angle ABC = \dots$ (in $^{\circ}$)

Prove that equal chords of congruent circles subtend equal angles at their centres.

$AB$ and $CD$ are two parallel chords of a circle with centre $P$. Also,the centre $P$ lies between the chords $AB$ and $CD$. If $AB = 20\,cm$,$CD = 48\,cm$,and the radius of the circle is $26\,cm$,find the distance between $AB$ and $CD$.

Write True or False and justify your answer.
The angles subtended by a chord at any two points of a circle are equal.

Prove that equal chords of a circle subtend equal angles at the centre.