In the figure above, the radius of circle with center O is 1

How do you know that BC is the base and AC is the height? Is it because on right angle triangle the 90 degree angle is never the base or the height? Bunuel

The altitude (height) of a triangle is the perpendicular from the base to the opposite vertex (the base may need to be extended). Since there are three possible bases, there are also three possible altitudes. In case of a right triangle both legs are altitudes as well as perpendicular from right angle to hypotenuse.
_________________

Usually it's always a GMAT rule that you should just assume ANYTHING...

The question only states that "the radius of the circle with center O is 1 and BC = 1".

How do I know that AC is the diameter? Yes, I see it on the graph but the graphs aren't accurate, are they? A could also be placed 1mm before the circle's line. It's not stated anywhere that the triangle is inscribed, is it?

Thanks for explaining!

First of all, if it were the way you are saying, how would you solve the question? It's a PS question, so one of the answers should be correct. How you get it?

Next, GMAT will not use such tricks. Check what is OG saying about the figures.

OFFICIAL GUIDE:

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.
_________________

Hi all,

Why can't AC be the base, and a vertical line drawn down from B, the height? I keep getting answer A, Sqrt(2)/(2).

The vertical line from B forms a smaller 45-45-90 triangle to the right, with BC as the hypotenuse, and the height of the entire triangle becomes 1/sqrt(2). Since the base is then 2 times radius, or 2, the Area = b*h/2, so the answer is A. Where am I going wrong?

A triangle has three bases, so yes you can consider AC to be the base. The problem is that the perpendicular from B to AC does not create 45-45-90 triangle. Check the image below:




_________________

A video explanation can be found here:
https://www.youtube.com/watch?v=QjP0s-vOXLY

Three of the many equations and facts you'll need to memorize for the GMAT are

- Area of a triangle = 1/2(base)(height)

- In a right triangle with angles 30-60-90 degrees, if the leg opposite the 30 degree angle has length a, then the hypotenuse has a length of 2a, and the other leg has a length of a√3 (see video below)

https://www.youtube.com/watch?v=QjP0s-vOXLY

- If a triangle inscribed in a circle has the diameter of the circle as one of its sides, that side will always be the hypotenuse, and the two legs that touch the circumference of the crcle will always interesect at 90 degrees (also best explained in video below)

Here we have hypotenuse = 2, therefore base = 1 and height = √3, therefore area = 1/2(1)(√3) = √3/2

Answer B.

Solution:

Since triangle ABC’s longest side, AC, is also the diameter of the circle, triangle ABC is a right triangle with right angle at B. Now, If we draw radius BO, then we have triangle BOC and it’s an equilateral triangle since BO = CO = BC = 1. Since triangle BOC is equilateral, angle C is 60 degrees. Therefore, triangle ABC is a 30-60-90 right triangle with the shortest side BC = 1. Thus, AB = 1 x √3 = √3 and the area of triangle ABC is ½ x 1 x √3 = √3/2.

Alternate Solution:

Triangle ABC is a right triangle with hypotenuse equal to the diameter of the circle, which is 2. One leg (BC) of the triangle has length 1. Thus, the length of AB is:

(AB)^2 + 1^2 = 2^2

(AB) = √3

The area of right triangle ABC is:

A = ½ (√3) x 1 = √3/2

Answer: B
_________________

Can we assume the hypotenuse of the triangle runs through the center of the circle if it is not stated?

AC is a diameter since it passes through the center of the circle. If a diameter forms one side of an inscribed triangle, then that triangle is necessarily a right triangle. The reverse is also true: in a right triangle inscribed in a circle, the hypotenuse will always coincide with the diameter of the circle.
_________________