1) What is a the greatest possible area of a triangular region with the vertex at the center of a circle with radius 1 and other two vertices on the circle
1) (sqrt 3)/4
5) sqrt 2
2) A certain circular area has its center at point P and has radius 4 and Points X & Y lie in the same plane as the circular area. Does point y lie outside the circular area. (Data Sufficiency)
1) Dist between X & P = 4.5
2) Disat between X & Y = 9
1) I am not sure this is so, can someone please confirm, that such a triangle of largest area is an equilateral one?
If that is the case, the answer is sqrt(3)/4.
Using special triangle properties the side of the triangle are in the ratio: 1:sqrt(3):2. [30:60:90]. Thus hyp is 1, so the height is sqrt(3)/2 and the base of the complete triangle is 1/2*2 = 1.
Thus the area is 1/2*1*sqrt(3)/2 = sqrt(3)/4.
The only way to do this is by drawing the circle, the center and the points X and Y.
1) X is obviously outside the circle because it is more than the radius away from the center. But doesnt say anything about Y. INSUFF.
2)Distance between X and Y is given, but this also insufficient since we have no indication about the location wrt the circle. INSUFF.
Together, it becomes clear that Y will always be outside the circle since the only way Y could have been at least on the circle would have been if X and Y were (4.5+4 = 8.5).
So, my answer is C.