Solution:
Given that a circle has radius cm. It is divided into two segments by a chord of length 2 cm. Then angle subtended by the chord at a point in the major segment is 55º.Creating figure using given data:
Now squaring on both sides of .
So, in triangle BOC we have,
Thus (By Converse of Pythagoras theorem).
So, subtends from the center O and angle at left segment of the circle,
Since the angle subtended by an arc at the center is double the angle subtended by it at any point on the left part of the circle, therefore .
As the angle subtended by the chord at a point in major segment is , thus statement is false.
Hence, option 2 is correct.