Hi hongwang9703,

There was a blog post the other day on this very topic. Basically, you should know that any triangle inscribed in a semicircle is always a right triangle. And you should know that GMAT can hide two similiar triangles in each other like the diagram in this problem!

Why are the triangles similiar to each other? This is because both triangles share angle A (so one angle is equal), and they both have a 90 degree angle. Therefore, the last angle for each triangle must be equal. Because all three angles are equal, they are similar.

Also, triangle ABC is similiar to CBD for the exact same reasons.

So what can you do with similiar triangles? You can set up porportions to find unknown sides. Take Statment 1 for instance.

BD = 5 and DC = 25/4. BC equals something (you COULD find with pythagorean theorum). BC is hypotonuse of smaller triangle, and AC is hypotonuse of larger triangle. This will give you AC:

DC / BC = BC / AC

OR

[second longest side of smaller triangle] / [second longest side of larger triangle] = [hypotonuse of smaller triangle] / [hypotonuse of larger triangle]

Viola, you can find AC if you really wanted to, but this is DS, so no messy calculation. Hizzah.

Repeat the process for Statement 2: you are basically given two legs of a triangle, so you can find the third, which combined with the fact the triangles are similiar gives you enough information to find AC.

Answer is D, as explanation says.