Angles in the same segment of a circle are equal - Proof
In this post, I will show you a couple of ways to prove that angles in the same segment of a circle are equal . The statement seems a little mysterious but the proofs are quite simple. So before going into any of the proofs, I want to quickly clarify the meaning of some of the terms occurring in the statement for those of you to whom the statement doesn’t seem to make sense. What is “segment” of a circle? Given a circle, draw a line that cuts across the circle. This line divides the circle into two regions. These regions are what we refer to as “segments” of the circle. The segment with the larger area is the major segment. The other segment of comparatively smaller area is the minor segment. The part of the borderline(circumference) of the circle that belongs to the major segment is the major arc, and the other part which belongs to the minor segment is the minor arc. What do we mean by “angle in a segment” of a circle? I will use letters P...