CAT (QA) PYQs

$ABCD$ is a quadrilateral inscribed in a circle with centre O. If $\angle COD = 120$ degrees and $\angle BAC = 30$ degrees, then the value of $\angle BCD$ (in degrees) is

In a circle of radius $11$ cm, $CD$ is a diameter and $AB$ is a chord of length $20.5$ cm. If $AB$ and $CD$ intersect at a point $E$ inside the circle and $CE$ has length $7$ cm, then the difference of the lengths of $BE$ and $AE$, in cm, is

In a triangle $ABC, AB = AC = 8$cm. $A$ circle drawn with $BC$ as diameter passes through $A$. Another circle drawn with center at $A$ passes through $B$ and $C$. Then the area, in sq. cm, of the overlapping region between the two circles is