DS - Geometry

[Maysaa]

I have a feeling I am missing the obvious, but can someone explain how ST1 below is sufficient?



Thanks
Maysaa

[GMATGuruNY]

In the figure shown, point O is the center of the semicircle and points B, C, and D lie on the semicircle. If the length of line segment AB is equal to the length of line sement OC, what is the degree measure of angle BAO?

(1) The degree measure of angle COD is 60.
(2) The degree measure of angle BCO is 40.

It is given that AB=OC.
Since OC and OB are both radii, OC=OB.
Thus:


EVALUATE THE EASIER STATEMENT FIRST.
Since statement 2 gives information about one of the equal angles, start with statement 2.

Statement 2: The degree measure of angle BCO is 40.
The result is the following combination of angles:

Thus, angle BAO = 20.
SUFFICIENT.

Statement 1: The degree measure of angle COD is 60.
In the combination of angles yielded by statement 2, angle COD = 60.
Thus, statement 1 implies the same combination of angles as does statement 2.
SUFFICIENT.

The correct answer is D.

[confused13]

one question:

since the triangle is within the circle, according to Thales' theorem one angle should have 90° right?

[GMATGuruNY]

one question:

since the triangle is within the circle, according to Thales' theorem one angle should have 90° right?

If a triangle is inscribed in a semi-circle such that one side of the triangle is also the diameter of the semi-circle, then the angle opposite the diameter will be a right angle, and the triangle will be a right triangle.
Here, the diameter does not serve as the side of a triangle, so the rule does not apply.