In same segment, if ∠ACB = 40°, find ∠ADB.
40°
Angles subtended by the same arc at the circumference, when the vertices lie in the same segment of a circle, are always equal.
In the given figure, points C and D lie in the same segment with respect to chord AB, so \(\angle ACB\) and \(\angle ADB\) are angles in the same segment.
By the angles-in-the-same-segment theorem, \(\angle ADB = \angle ACB = 40^\circ\).
In a circle, AB is a chord. If ∠ACB = 50°, find ∠ADB.

ABCD is a cyclic quadrilateral. If ∠A = 70°, find ∠C.

How many tangents can be drawn to a circle from a point outside it?
There are two concentric circles. The radii of the two circles are 100 m and 110 m respectively. A wheel of radius 30 cm rolls on the smaller circle and another wheel rolls on the larger circle. After they have completed one revolution, it is found that the two wheels rolled equal number of times
on their respective axes. What is the radius of the other wheel ?