In the diagram, A, X, B, C, D are points on the circle. AD is the diameter of the smaller circle. Find the angles AXD and ABC.

Angle $AXD$ is an angle subtended by the diameter $AD$ at the circumference of the smaller circle.

The angle subtended by a diameter at any point on the circumference is $90^\circ$.

Reason: Angle in a semicircle.
The value of Angle $AXD$ is $\boxed{90^\circ}$.

$ABCD$ is a cyclic quadrilateral in the bigger circle.