In a circle, AB and CD are diameters. Which of the following must be true?
I. The length of arc ABD is equal to the length of arc BAC
II. AB is perpendicular to CD
III. ACBD is a square
Above is an image that shows that II and III don’t have to be true. You can trace arcs ABD and BAC, and you’ll see that they are in fact both the same–they’re the whole circle except the tiny arcs BC and AD, which must be equal because their corresponding central angles are vertical angles.
Comments (2)
i was confused about this question because the ordering of the arc. shouldn’t it be arc ACB, not BAC? for arc BAC, the points are not in order so I was confused.
Trust the orders given. These are very long arcs. Almost all the way around the circle.