Steven1604 wrote:

I see the options A,B and D are different representations of the same. But why could the answer not be any one of these? Also is it really necessary to know the angle to find the area of the triangle? isn't the base and height enough? please explain. Thank you!

Steven1604,

The area of a triangle are dependent on base and height. But for a triangle with one vertex at the circle and two points on the circle, both height & base depend on the angle it subtends at the center. Instead of going into the math - just imagine a triangle with base which is very small such that the triangle is barely visible ( here the angle at the center would be close to zero ) vs. a triangle with angle > 90 at center would be much larger..

Without thinking about the base and the height here - we know for sure a smaller triangle ill have a smaller area... so the ratio of areas cannot be found!

Hope this makes sense.

Regards,

G