guenthermat wrote:
Bunuel wrote:
abhas59 wrote:
In the figure above, the radius of circle with center O is 1 and BC = 1. What is the area of triangular region ABC ?
Hi guys,
Just one doubt, how can we say that triangle ABC is a right angled triangle given the radius is one & other side BC is one.
I mean to say that is there any property for circle that if radius is equal to any one side of the triangle, then the inscribed triangle so formed will be right-angled one?
We know that AC is a diameter. There is a property of a right triangle inscribed in circle:
A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle and diameter is hypotenuse.
Attachment:
Math_Tri_inscribed.png
Hope it helps.
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 SolvingFigures: 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.
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