Hi, Asma.

This question seems incomplete. Are you sure this was transcribed correctly?

yes, it is I found it in gmat club and it is from Magoosh

this is the link

https://gmatclub.com/forum/if-the-circle ... 93822.html

I see. (The image didn't come up on this site the first time.) The reason you'd need Statement 2 is that, according to the original diagram, we don't know that BC is the diameter. It may just be a random chord, in which case, there's no way to know how long it is. (And we also wouldn't know the measure of the inscribed angle opposite BC.) Once we're told that BC = 12, we know it's the diameter, which also tells us that the inscribed angle opposite BC is 90 degrees.

Here was the original image that didn't show up initially:

but in the question the radius is equal to 6 so already BC equal to 12 i do not understand what you

mean when you say ((It may just be a random chord))? can you show me where is the radius in this

circle if it is not the half of BC? I realy confused!!!!!!

What's confusing is that in the original picture, BC is drawn to look like the diameter, but because we can't assume that anything on the GMAT is drawn to scale, it's possible that BC is a chord that isn't the diameter, but merely appears that way.

Consider the image below.



Let's say that the black line is the diameter, and is therefore equal to 12. The blue chord will be a little smaller than 12. The green chord will be smaller than the blue. And the yellow chord will be smaller than the green, and so on, the chords getting progressively smaller as we move away from the diameter. Because we aren't initially told that BC is the diameter, technically, BC could be any of those lines. Maybe it's equal to 11 or 10, and is simply close to the diameter. As far as we know, it only looks like the diameter. We can't assume anything. We need to be told either that BC is the diameter or that it's equal to 12. Does that make more sense?

TKANK YOU SO MUCH I SEE KNOW WHAT YOU MEAN