**Quote:**

If points \(A\) , \(B\) , and \(C\) lie on a circle of radius 1, what is the area of triangle \(ABC\) ?

1. \(AB^2 = BC^2 + AC^2\)

2. \(\angle CAB\) equals 30 degrees

(C) 2008 GMAT Club - Geometry - II#3

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient

* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient

* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

* EACH statement ALONE is sufficient

* Statements (1) and (2) TOGETHER are NOT sufficient

Statements(1) and (2) combined are sufficient. S1 and S2 define the shape of the triangle. Because this triangle can be inscribed in a circle of radius 1, we also know the size of the triangle. There is only one triangle with a given shape and size.

I understand that there's only one possible triangle with that given shape, but how can you know the area?

Also:

**Quote:**

If the area of a rectangle is 80, what is the angle between the diagonal of the rectangle and its longer side?

1. The perimeter of the rectangle is 84

2. The shorter side of the rectangle is 2

(C) 2008 GMAT Club - Geometry - II#9

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient

* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient

* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

* EACH statement ALONE is sufficient

* Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is sufficient. We can find the sides of the rectangle (40 and 2).

Statement (2) by itself is sufficient. We can find the sides of the rectangle (40 and 2).

The correct answer is D.

We know the sides but what about the angle between the diagonal and the longer side?

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