linkinpark wrote:
I think you're guessing based on the given drawing, but don't assume anything unless it's mentioned implicitly or it can be drawn out from given information.
in A it says angle is 30 but we don't know yet if the triangle is right angled so its insufficient.
This is an incredibly important principle for data sufficiency: don't assume anything (well, almost nothing).
One key difference between PS and DS is geometry diagrams.
In PS, diagrams are, by default, drawn to scale; unless they specifically state otherwise, you can rely on how diagrams look to help you answer questions.
In DS, on the other hand, diagrams are NOT drawn to scale; we can only rely on information that we're specifically given.
So, in this particular question, it looks like AB is a diameter of the circle, but until we're explicitly (or implicitly) told that AB is the diameter, it's just a random chord of the circle.
Once we know it's the diameter from (2), we know that ABC is a right triangle (any triangle formed inside the circle by the diameter and a point on the circumference will be right). However, by itself that's not enough info, since there are an infinite number of different right triangles we can form with the diameter as the hypotenuse.
Adding (1) into the equation, we know we have a 30/60/90 triangle and we know one of the sides, so we can figure out whatever we want about the triangle.