If the circle has radius 6, what is the area of the triangle? (1) AC

MAGOOSH OFFICIAL SOLUTION:

can any one please show me what is the new information that we got from statement 2 where we already know from the

question that BC=12 . so statement 1 is suff.

Hi,
statement 1 does not reveal anything about BC. We don't know if BC is a diameter.


Kudos if this helps!

Hi dear, but in the question the radius is equal to 6 so already BC equal to 12 ? can you show me where is the radius in

this circle if it is not the half of BC? I realy confused!!!!!!

Hi 23a2012,

In DS questions, a good rule to remember is that the "picture is NOT necessarily drawn to scale" (in real basic terms, you CANNOT trust the picture). You CAN trust numbers and you CAN trust data, but a drawing might not be accurate (and sometimes the given drawing is REALLY inaccurate).

In the drawing that comes with this question, BC "looks like" it could be the diameter, but we don't know for sure if it actually is the diameter (it might be a little shorter than the diameter or possibly a LOT shorter than the diameter. In the prompt, we're told that the radius = 6 and in Fact 2, we're told that BC = 12. THOSE pieces of data prove that BC is the diameter, but without BOTH of those pieces of information, we would not know that that was the case.

GMAT assassins aren't born, they're made,
Rich

I chose B.
Because we know the diameter of the circle and the distance from the center to Point A equals the radius, which we can take for the height of the triangle.

Where did I make the mistake?

Many thanks in advance!

I chose B.
Because we know the diameter of the circle and the distance from the center to Point A equals the radius, which we can take for the height of the triangle.

Where did I make the mistake?

Many thanks in advance!

Hi marcoelmanchi,

To calculate the area of a triangle, we need to know the BASE and the HEIGHT of the triangle. It's important to remember that the height of a triangle is PERPENDICULAR to the base (meaning that a 90 degree angle must be formed between the base and the height). With the information in Fact 2, we can 'spin' the triangle around so that the diameter is the base - so we know that the base = 12. However, we do NOT know what the height is. It COULD be 6, but it could be LESS than 6. Thus, there's more than one possible answer and Fact 2 is INSUFFICIENT.

GMAT assassins aren't born, they're made,
Rich

If the circle has radius 6, what is the area of the triangle?

(1) AC = AB

(2) BC = 12

Take away:

We do not know whether BC is infact the diameter, the pictures aren't drawn to scale and it can be deceptive. We know the radius is 6 and statement 2 provides us with the length of a chord = 12, which is twice the radius, hence, BC must be the diameter.

Although this question is not that difficult, conceptually, the diagram provided provides the trick element in this question. It is very easy to fall into the trap of assuming it to be a right angled triangle because it looks like one.

Remember, unless until the question says explicitly that the triangle is right angled, you are not supposed to assume it is.

From the question statement, we know that the radius of the circle is 6. The area of the triangle can be calculated if we can find out the unique values of AB and AC.

From statement I alone, we can only say that the triangle is an isosceles triangle. We do not know anything about BC nor do we know the values of AB and AC. So, this statement is insufficient. Options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, we can only say that BC is the diameter of the circle. We can also say that ABC is a right angled triangle (angle in a semicircle is a right angle) , but we have no data about the other two sides. Hence, we cannot obtain a unique figure and so, a unique answer. Option B can be eliminated.

Combining statements I and II, we can conclude that triangle ABC is an isosceles right angled triangle with hypotenuse 12. This is clearly sufficient to find out AB and AC and hence the area of the triangle.
The correct answer option is C.

Remember, in questions like these, it is very easy to fall into the trap of assuming that the figure is a right angled triangle. The idea is to stick to the basic rule of DS and try to evaluate the individual statements alone.

Hope this helps!